Quizbank/Electricity and Magnetism: Gauss' Law/Cum

calcPhyEM_2GaussQuizzes/Cum ID153728160820

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Exams:  A0  A1  A2   B0  B1  B2   C0  C1  C2   D0  D1  D2   E0  E1  E2   F0  F1  F2   G0  G1  G2   H0  H1  H2   I0  I1  I2   J0  J1  J2   K0  K1  K2   L0  L1  L2   M0  M1  M2   N0  N1  N2   O0  O1  O2   P0  P1  P2   Q0  Q1  Q2   R0  R1  R2   S0  S1  S2   T0  T1  T2  

Answers:   A0  A1  A2   B0  B1  B2   C0  C1  C2   D0  D1  D2   E0  E1  E2   F0  F1  F2   G0  G1  G2   H0  H1  H2   I0  I1  I2   J0  J1  J2   K0  K1  K2   L0  L1  L2   M0  M1  M2   N0  N1  N2   O0  O1  O2   P0  P1  P2   Q0  Q1  Q2   R0  R1  R2   S0  S1  S2   T0  T1  T2  

60 Tests = 3 versions x 20 variations: Each of the 20 variations (A, B, ...) represents a different random selection of questions taken from the study guide.The 3 versions (0,1,..) all have the same questions but in different order and with different numerical inputs. Unless all students take version "0" it is best to reserve it for the instructor because the questions are grouped according to the order in which they appear on the study guide.

Links:   Quizbank/Instructions   Study guide   file:QB-calcPhyEM_2GaussQuizzes-Cum.pdf

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Cum A0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) none of these are correct

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) none of these are correct

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

Cum A1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction over a portion of the Gaussian surface

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

5) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho$

Cum A2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant direction over a portion of the Gaussian surface

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

5) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

6) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2\varepsilon _{0}E=r\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho /2$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

Cum B0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) none of these are correct

e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant in direction over the entire Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

Cum B1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) none of these are correct

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho /2$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho /2$

e) none of these are correct

6) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction over a portion of the Gaussian surface

Cum B2

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) none of these are correct

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho /2$

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant direction over a portion of the Gaussian surface

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=\rho z$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

Cum C0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho /2$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) none of these are correct

d) $2\varepsilon _{0}E=r\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum C1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) none of these are correct

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=\rho z$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho z$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2\varepsilon _{0}E=r\rho$

Cum C2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) none of these are correct

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant direction over a portion of the Gaussian surface

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=\rho z$

Cum D0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) none of these are correct

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant direction over a portion of the Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

Cum D1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho /2$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho z$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) none of these are correct

5) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) none of these are correct

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant in direction over the entire Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=H\rho /2$

Cum D2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) none of these are correct

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho z$

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

Cum E0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho z$

e) none of these are correct

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) none of these are correct

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction over a portion of the Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum E1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) none of these are correct

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=H\rho$

8) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=H\rho$

d) none of these are correct

e) $\varepsilon _{0}E=\rho z$

Cum E2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho /2$

c) none of these are correct

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho z$

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

7) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) none of these are correct

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho$

e) none of these are correct

Cum F0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho /2$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum F1

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) none of these are correct

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) none of these are correct

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=\rho z$

e) none of these are correct

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant direction over a portion of the Gaussian surface

10) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

Cum F2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) none of these are correct

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) none of these are correct

e) $\varepsilon _{0}E=\rho z$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) none of these are correct

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2\varepsilon _{0}E=r\rho$

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) none of these are correct

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

Cum G0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho /2$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) none of these are correct

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum G1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant in direction over the entire Gaussian surface

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) none of these are correct

e) $2R\varepsilon _{0}E=r^{2}\rho$

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) none of these are correct

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) none of these are correct

c) $2\varepsilon _{0}E=r\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

9) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho /2$

Cum G2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) none of these are correct

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho$

Cum H0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho z$

e) none of these are correct

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant in direction over the entire Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

Cum H1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) none of these are correct

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant direction over a portion of the Gaussian surface

Cum H2

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho /2$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) none of these are correct

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) none of these are correct

c) $2\varepsilon _{0}E=r\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=\rho z$

e) none of these are correct

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

Cum I0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=\rho z$

e) none of these are correct

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum I1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) none of these are correct

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

7) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho z$

e) none of these are correct

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho$

d) none of these are correct

e) $\varepsilon _{0}E=\rho z$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

Cum I2

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho /2$

c) none of these are correct

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho z$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho /2$

e) none of these are correct

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) none of these are correct

e) $2R\varepsilon _{0}E=r^{2}\rho$

Cum J0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) none of these are correct

e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant direction over a portion of the Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum J1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) none of these are correct

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=H\rho$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho z$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) none of these are correct

d) $2\varepsilon _{0}E=r\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho /2$

e) none of these are correct

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

Cum J2

1) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) none of these are correct

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant in direction over the entire Gaussian surface

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2\varepsilon _{0}E=r\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho$

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho /2$

e) none of these are correct

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) none of these are correct

e) $2R\varepsilon _{0}E=r^{2}\rho$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

Cum K0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2\varepsilon _{0}E=r\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum K1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) none of these are correct

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) $2\varepsilon _{0}E=r\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho$

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho z$

e) none of these are correct

10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) none of these are correct

Cum K2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=H\rho$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho z$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant in direction over the entire Gaussian surface

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho /2$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2\varepsilon _{0}E=r\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) none of these are correct

d) $2\varepsilon _{0}E=r\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

Cum L0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho$

e) none of these are correct

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) none of these are correct

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) none of these are correct

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

Cum L1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) none of these are correct

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=\rho z$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

Cum L2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

4) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) none of these are correct

5) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho /2$

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) none of these are correct

d) $2\varepsilon _{0}E=r\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

Cum M0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=H\rho /2$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) none of these are correct

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

Cum M1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) none of these are correct

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2\varepsilon _{0}E=r\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

5) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) none of these are correct

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=H\rho$

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=H\rho /2$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

Cum M2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=H\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho /2$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) none of these are correct

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho z$

e) none of these are correct

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

Cum N0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho /2$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=H\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) none of these are correct

e) $2r\varepsilon _{0}E=R^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

Cum N1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) none of these are correct

c) $2\varepsilon _{0}E=r\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) none of these are correct

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

Cum N2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho /2$

c) $\varepsilon _{0}E=\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho z$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) none of these are correct

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho /2$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

Cum O0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho z$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) none of these are correct

d) $2\varepsilon _{0}E=r\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2\varepsilon _{0}E=r\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum O1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho z$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

7) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) none of these are correct

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2\varepsilon _{0}E=r\rho$

Cum O2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho /2$

e) none of these are correct

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) none of these are correct

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

7) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) none of these are correct

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) none of these are correct

Cum P0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho$

e) none of these are correct

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) none of these are correct

e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum P1

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=H\rho$

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) none of these are correct

c) $2\varepsilon _{0}E=r\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

Cum P2

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

5) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho /2$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) none of these are correct

c) $2\varepsilon _{0}E=r\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction over a portion of the Gaussian surface

Cum Q0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) none of these are correct

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum Q1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho z$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho /2$

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r\varepsilon _{0}E=R^{2}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) none of these are correct

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) none of these are correct

Cum Q2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) none of these are correct

e) $2r\varepsilon _{0}E=R^{2}\rho$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=\rho z$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

6) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho z$

e) none of these are correct

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) $2\varepsilon _{0}E=r\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

Cum R0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) $\varepsilon _{0}E=H\rho$

c) $\varepsilon _{0}E=H\rho /2$

d) none of these are correct

e) $\varepsilon _{0}E=\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) none of these are correct

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant direction and magnitude over the entire Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum R1

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) none of these are correct

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant direction over a portion of the Gaussian surface

c) constant in direction over the entire Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=H\rho /2$

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=H\rho$

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

Cum R2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=\rho z$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

a) True

b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) none of these are correct

c) $2\varepsilon _{0}E=r\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2\varepsilon _{0}E=r\rho$

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) none of these are correct

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=H\rho$

b) none of these are correct

c) $\varepsilon _{0}E=\rho z$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

9) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant magnitude over a portion of the Gaussian surface

d) constant direction over a portion of the Gaussian surface

Cum S0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho /2$

b) $\varepsilon _{0}E=H\rho$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=\rho z$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) none of these are correct

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2R\varepsilon _{0}E=r^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) none of these are correct

d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant in direction over the entire Gaussian surface

b) constant magnitude over a portion of the Gaussian surface

c) constant direction and magnitude over the entire Gaussian surface

d) constant direction over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

Cum S1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=\rho z$

e) $\varepsilon _{0}E=H\rho$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant direction and magnitude over the entire Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant magnitude over a portion of the Gaussian surface

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) $2r\varepsilon _{0}E=R^{2}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) none of these are correct

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2\varepsilon _{0}E=r\rho$

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) none of these are correct

e) $2R\varepsilon _{0}E=r^{2}\rho$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

b) none of these are correct

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

Cum S2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) none of these are correct

c) $2\varepsilon _{0}E=r\rho$

d) $2R\varepsilon _{0}E=r^{2}\rho$

e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) none of these are correct

e) $\varepsilon _{0}E=H\rho$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

4) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

a) constant magnitude over a portion of the Gaussian surface

b) constant in direction over the entire Gaussian surface

c) constant direction over a portion of the Gaussian surface

d) constant direction and magnitude over the entire Gaussian surface

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) none of these are correct

c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

d) $2\varepsilon _{0}E=r\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

e) none of these are correct

Cum T0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) $\varepsilon _{0}E=H\rho z$

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=\rho z$

e) none of these are correct

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r\varepsilon _{0}E=R^{2}\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) $2R\varepsilon _{0}E=r^{2}\rho$

d) none of these are correct

e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

Cum T1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=\rho z$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho z$

d) $\varepsilon _{0}E=H\rho$

e) $\varepsilon _{0}E=H\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) $\varepsilon _{0}E=\rho z$

b) $\varepsilon _{0}E=H\rho$

c) none of these are correct

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

b) $2R\varepsilon _{0}E=r^{2}\rho$

c) none of these are correct

d) $2\varepsilon _{0}E=r\rho$

e) $2r\varepsilon _{0}E=R^{2}\rho$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

10) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

Cum T2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

a) True

b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

a) True

b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) $\varepsilon _{0}E=H\rho$

b) none of these are correct

c) $\varepsilon _{0}E=H\rho /2$

d) $\varepsilon _{0}E=H\rho z$

e) $\varepsilon _{0}E=\rho z$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

a) none of these are correct

b) $\varepsilon _{0}E=\rho z$

c) $\varepsilon _{0}E=H\rho$

d) $\varepsilon _{0}E=H\rho /2$

e) $\varepsilon _{0}E=H\rho z$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

a) True

b) False

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

c) none of these are correct

d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) $2\varepsilon _{0}E=r\rho$

b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

c) none of these are correct

d) $2r\varepsilon _{0}E=R^{2}\rho$

e) $2R\varepsilon _{0}E=r^{2}\rho$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

d) none of these are correct

e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

a) True

b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

a) True

b) False

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Key: A0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho z$

-c) none of these are correct

+d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho$

+d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) none of these are correct

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) none of these are correct

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant in direction over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

Key: A1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant in direction over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction over a portion of the Gaussian surface

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

5) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2\varepsilon _{0}E=r\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho$

Key: A2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

+d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant in direction over the entire Gaussian surface

-d) constant direction over a portion of the Gaussian surface

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

5) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

6) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) none of these are correct

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

+d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2\varepsilon _{0}E=r\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=\rho z$

+e) $\varepsilon _{0}E=H\rho /2$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

Key: B0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) none of these are correct

-b) $\varepsilon _{0}E=H\rho z$

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho /2$

+e) $\varepsilon _{0}E=\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) none of these are correct

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) none of these are correct

+e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant direction over a portion of the Gaussian surface

-d) constant in direction over the entire Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

Key: B1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) none of these are correct

-c) $2R\varepsilon _{0}E=r^{2}\rho$

+d) $2\varepsilon _{0}E=r\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho z$

+c) $\varepsilon _{0}E=\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho /2$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho$

+d) $\varepsilon _{0}E=H\rho /2$

-e) none of these are correct

6) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) none of these are correct

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction over a portion of the Gaussian surface

Key: B2

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) none of these are correct

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho z$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=H\rho /2$

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

-d) constant direction over a portion of the Gaussian surface

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=\rho z$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

Key: C0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) none of these are correct

-c) $\varepsilon _{0}E=\rho z$

-d) $\varepsilon _{0}E=H\rho$

+e) $\varepsilon _{0}E=H\rho /2$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

-b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho$

+e) $\varepsilon _{0}E=\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) none of these are correct

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) none of these are correct

+d) $2\varepsilon _{0}E=r\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

+b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2\varepsilon _{0}E=r\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: C1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

+b) $2\varepsilon _{0}E=r\rho$

-c) none of these are correct

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) none of these are correct

+b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=\rho z$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho$

+d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho z$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction over a portion of the Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2\varepsilon _{0}E=r\rho$

Key: C2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=H\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) none of these are correct

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant in direction over the entire Gaussian surface

-d) constant direction over a portion of the Gaussian surface

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=\rho z$

Key: D0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=\rho z$

-c) none of these are correct

+d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) none of these are correct

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+b) $2\varepsilon _{0}E=r\rho$

-c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) none of these are correct

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2\varepsilon _{0}E=r\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

-c) constant in direction over the entire Gaussian surface

-d) constant direction over a portion of the Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

Key: D1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

+b) $\varepsilon _{0}E=H\rho /2$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=H\rho z$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) none of these are correct

5) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) none of these are correct

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2\varepsilon _{0}E=r\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant direction over a portion of the Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant in direction over the entire Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=H\rho /2$

Key: D2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) none of these are correct

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

+b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho z$

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

+d) $2\varepsilon _{0}E=r\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction over a portion of the Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

Key: E0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

+b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=\rho z$

-d) $\varepsilon _{0}E=H\rho z$

-e) none of these are correct

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) none of these are correct

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant in direction over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction over a portion of the Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: E1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) none of these are correct

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2r\varepsilon _{0}E=R^{2}\rho$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=H\rho$

8) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

+a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant direction over a portion of the Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

+b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=H\rho$

-d) none of these are correct

-e) $\varepsilon _{0}E=\rho z$

Key: E2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

-c) constant in direction over the entire Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

+b) $\varepsilon _{0}E=H\rho /2$

-c) none of these are correct

-d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho z$

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) none of these are correct

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

7) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) none of these are correct

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho z$

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho$

-e) none of these are correct

Key: F0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=\rho z$

-d) none of these are correct

+e) $\varepsilon _{0}E=H\rho /2$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) none of these are correct

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

+b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant direction over a portion of the Gaussian surface

-c) constant in direction over the entire Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: F1

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) none of these are correct

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2\varepsilon _{0}E=r\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) none of these are correct

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=\rho z$

-e) none of these are correct

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

-c) constant in direction over the entire Gaussian surface

-d) constant direction over a portion of the Gaussian surface

10) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

+a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

Key: F2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2\varepsilon _{0}E=r\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) none of these are correct

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho z$

+c) $\varepsilon _{0}E=H\rho /2$

-d) none of these are correct

-e) $\varepsilon _{0}E=\rho z$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) none of these are correct

-d) $2R\varepsilon _{0}E=r^{2}\rho$

+e) $2\varepsilon _{0}E=r\rho$

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant direction over a portion of the Gaussian surface

-c) constant in direction over the entire Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) none of these are correct

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

Key: G0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) none of these are correct

-b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho$

+e) $\varepsilon _{0}E=H\rho /2$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) none of these are correct

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) none of these are correct

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2r\varepsilon _{0}E=R^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

+b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: G1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant in direction over the entire Gaussian surface

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) none of these are correct

-e) $2R\varepsilon _{0}E=r^{2}\rho$

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) none of these are correct

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) none of these are correct

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

9) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) none of these are correct

+e) $\varepsilon _{0}E=H\rho /2$

Key: G2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant direction over a portion of the Gaussian surface

-c) constant in direction over the entire Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+b) $2\varepsilon _{0}E=r\rho$

-c) none of these are correct

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) none of these are correct

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=\rho z$

+d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho$

Key: H0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

+b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=\rho z$

-d) $\varepsilon _{0}E=H\rho z$

-e) none of these are correct

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

+d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

+d) $2\varepsilon _{0}E=r\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

+b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant direction over a portion of the Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

-d) constant in direction over the entire Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

Key: H1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2\varepsilon _{0}E=r\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

+d) $2\varepsilon _{0}E=r\rho$

-e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho$

-c) $\varepsilon _{0}E=H\rho z$

+d) $\varepsilon _{0}E=\rho z$

-e) none of these are correct

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho$

-c) none of these are correct

+d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

-d) constant direction over a portion of the Gaussian surface

Key: H2

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction over a portion of the Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) none of these are correct

-b) $\varepsilon _{0}E=H\rho$

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=\rho z$

+e) $\varepsilon _{0}E=H\rho /2$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) none of these are correct

+d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) none of these are correct

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=H\rho /2$

+d) $\varepsilon _{0}E=\rho z$

-e) none of these are correct

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

Key: I0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho z$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=H\rho$

+d) $\varepsilon _{0}E=\rho z$

-e) none of these are correct

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) none of these are correct

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

+b) $2\varepsilon _{0}E=r\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: I1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) none of these are correct

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

7) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho /2$

+c) $\varepsilon _{0}E=\rho z$

-d) $\varepsilon _{0}E=H\rho z$

-e) none of these are correct

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) none of these are correct

-e) $\varepsilon _{0}E=\rho z$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

-c) constant direction over a portion of the Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

Key: I2

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

+b) $\varepsilon _{0}E=H\rho /2$

-c) none of these are correct

-d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho z$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction over a portion of the Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho$

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho /2$

-e) none of these are correct

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) none of these are correct

-e) $2R\varepsilon _{0}E=r^{2}\rho$

Key: J0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) none of these are correct

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=H\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

+d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) none of these are correct

-e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

-d) constant direction over a portion of the Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: J1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) none of these are correct

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=H\rho$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho z$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) none of these are correct

-d) $2\varepsilon _{0}E=r\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction over a portion of the Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=H\rho$

+d) $\varepsilon _{0}E=H\rho /2$

-e) none of these are correct

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

Key: J2

1) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) none of these are correct

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant direction over a portion of the Gaussian surface

-d) constant in direction over the entire Gaussian surface

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

-b) $2\varepsilon _{0}E=r\rho$

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) $\varepsilon _{0}E=H\rho /2$

+c) $\varepsilon _{0}E=\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho$

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho$

+d) $\varepsilon _{0}E=H\rho /2$

-e) none of these are correct

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) none of these are correct

-e) $2R\varepsilon _{0}E=r^{2}\rho$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

Key: K0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) none of these are correct

-b) $\varepsilon _{0}E=H\rho$

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

+b) $\varepsilon _{0}E=\rho z$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=H\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) none of these are correct

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct

-b) $2R\varepsilon _{0}E=r^{2}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

-b) $2\varepsilon _{0}E=r\rho$

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: K1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

+b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2\varepsilon _{0}E=r\rho$

-e) none of these are correct

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct

+b) $2\varepsilon _{0}E=r\rho$

-c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

-c) constant direction over a portion of the Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho$

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho$

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho z$

-e) none of these are correct

10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) none of these are correct

Key: K2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

+b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=H\rho$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho z$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

-d) constant in direction over the entire Gaussian surface

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

+d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho /2$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

+e) $2\varepsilon _{0}E=r\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) none of these are correct

-d) $2\varepsilon _{0}E=r\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

Key: L0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

+b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=\rho z$

-d) $\varepsilon _{0}E=H\rho$

-e) none of these are correct

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) none of these are correct

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r\varepsilon _{0}E=R^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) none of these are correct

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

Key: L1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) none of these are correct

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho z$

-c) none of these are correct

+d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=\rho z$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2\varepsilon _{0}E=r\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) none of these are correct

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

Key: L2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

4) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

+a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) none of these are correct

5) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) none of these are correct

-b) $\varepsilon _{0}E=H\rho$

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=\rho z$

+e) $\varepsilon _{0}E=H\rho /2$

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) none of these are correct

+d) $2\varepsilon _{0}E=r\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

+b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2\varepsilon _{0}E=r\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

Key: M0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

+b) $\varepsilon _{0}E=H\rho /2$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

+d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) none of these are correct

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+d) $2\varepsilon _{0}E=r\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

Key: M1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) none of these are correct

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+e) $2\varepsilon _{0}E=r\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

5) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) none of these are correct

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

-b) $\varepsilon _{0}E=H\rho /2$

+c) $\varepsilon _{0}E=\rho z$

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=H\rho$

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=\rho z$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho z$

+e) $\varepsilon _{0}E=H\rho /2$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

Key: M2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho$

-c) $\varepsilon _{0}E=H\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho /2$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) none of these are correct

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho$

-c) $\varepsilon _{0}E=\rho z$

-d) $\varepsilon _{0}E=H\rho z$

-e) none of these are correct

7) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

9) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

Key: N0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) none of these are correct

+e) $\varepsilon _{0}E=H\rho /2$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho /2$

-c) $\varepsilon _{0}E=H\rho z$

-d) none of these are correct

+e) $\varepsilon _{0}E=\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) none of these are correct

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) none of these are correct

+e) $2r\varepsilon _{0}E=R^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

Key: N1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

2) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho z$

-c) none of these are correct

+d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) none of these are correct

+c) $2\varepsilon _{0}E=r\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r\varepsilon _{0}E=R^{2}\rho$

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) none of these are correct

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

Key: N2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho /2$

+c) $\varepsilon _{0}E=\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho z$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) none of these are correct

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) none of these are correct

+e) $\varepsilon _{0}E=H\rho /2$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

Key: O0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=H\rho z$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) none of these are correct

+d) $2\varepsilon _{0}E=r\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

-b) $2\varepsilon _{0}E=r\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: O1

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho /2$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho z$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2\varepsilon _{0}E=r\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

7) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) none of these are correct

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction over a portion of the Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) none of these are correct

-d) $2r\varepsilon _{0}E=R^{2}\rho$

+e) $2\varepsilon _{0}E=r\rho$

Key: O2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=H\rho /2$

-e) none of these are correct

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) none of these are correct

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2\varepsilon _{0}E=r\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant in direction over the entire Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

7) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) none of these are correct

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct

-b) $2r\varepsilon _{0}E=R^{2}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) none of these are correct

Key: P0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho z$

-c) $\varepsilon _{0}E=\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho z$

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho$

-e) none of these are correct

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2\varepsilon _{0}E=r\rho$

-d) none of these are correct

-e) $2R\varepsilon _{0}E=r^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction over a portion of the Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: P1

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) none of these are correct

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=H\rho$

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho z$

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho /2$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) none of these are correct

-c) $2\varepsilon _{0}E=r\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

Key: P2

1) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

5) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho z$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho /2$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho z$

-c) none of these are correct

+d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) none of these are correct

-c) $2\varepsilon _{0}E=r\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant in direction over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction over a portion of the Gaussian surface

Key: Q0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) $\varepsilon _{0}E=\rho z$

-c) none of these are correct

+d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho z$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho /2$

+e) $\varepsilon _{0}E=\rho z$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) none of these are correct

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: Q1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho z$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho z$

-d) none of these are correct

+e) $\varepsilon _{0}E=H\rho /2$

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

+b) $2r\varepsilon _{0}E=R^{2}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) none of these are correct

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

+b) $2\varepsilon _{0}E=r\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) none of these are correct

Key: Q2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2\varepsilon _{0}E=r\rho$

-d) none of these are correct

+e) $2r\varepsilon _{0}E=R^{2}\rho$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho$

-e) $\varepsilon _{0}E=\rho z$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

6) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=H\rho z$

-e) none of these are correct

10) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct

+b) $2\varepsilon _{0}E=r\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

Key: R0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) $\varepsilon _{0}E=H\rho$

+c) $\varepsilon _{0}E=H\rho /2$

-d) none of these are correct

-e) $\varepsilon _{0}E=\rho z$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho /2$

+b) $\varepsilon _{0}E=\rho z$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) none of these are correct

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) none of these are correct

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) none of these are correct

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

-b) constant direction and magnitude over the entire Gaussian surface

-c) constant direction over a portion of the Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: R1

1) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) none of these are correct

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+d) $2\varepsilon _{0}E=r\rho$

-e) $2r\varepsilon _{0}E=R^{2}\rho$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant direction over a portion of the Gaussian surface

-c) constant in direction over the entire Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

+b) $\varepsilon _{0}E=\rho z$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=H\rho /2$

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) none of these are correct

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) $2\varepsilon _{0}E=r\rho$

+d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

9) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) none of these are correct

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=H\rho$

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

Key: R2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=\rho z$

-c) none of these are correct

+d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

3) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated inside the Gaussian surface

-a) True

+b) False

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) none of these are correct

-c) $2\varepsilon _{0}E=r\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+c) $2\varepsilon _{0}E=r\rho$

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) none of these are correct

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) none of these are correct

+c) $\varepsilon _{0}E=\rho z$

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

9) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

10) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant in direction over the entire Gaussian surface

+c) constant magnitude over a portion of the Gaussian surface

-d) constant direction over a portion of the Gaussian surface

Key: S0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

+a) $\varepsilon _{0}E=H\rho /2$

-b) $\varepsilon _{0}E=H\rho$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=\rho z$

2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

+a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) none of these are correct

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

+a) $2\varepsilon _{0}E=r\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) none of these are correct

-d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2R\varepsilon _{0}E=r^{2}\rho$

-b) $2\varepsilon _{0}E=r\rho$

-c) none of these are correct

-d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant in direction over the entire Gaussian surface

+b) constant magnitude over a portion of the Gaussian surface

-c) constant direction and magnitude over the entire Gaussian surface

-d) constant direction over a portion of the Gaussian surface

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

Key: S1

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho z$

-b) none of these are correct

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=\rho z$

-e) $\varepsilon _{0}E=H\rho$

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

-a) constant direction and magnitude over the entire Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction over a portion of the Gaussian surface

+d) constant magnitude over a portion of the Gaussian surface

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

4) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

5) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

+c) $2r\varepsilon _{0}E=R^{2}\rho$

-d) $2\varepsilon _{0}E=r\rho$

-e) none of these are correct

8) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

+b) $2\varepsilon _{0}E=r\rho$

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) none of these are correct

-e) $2R\varepsilon _{0}E=r^{2}\rho$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-b) none of these are correct

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

Key: S2

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) none of these are correct

+c) $2\varepsilon _{0}E=r\rho$

-d) $2R\varepsilon _{0}E=r^{2}\rho$

-e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho z$

+c) $\varepsilon _{0}E=H\rho /2$

-d) none of these are correct

-e) $\varepsilon _{0}E=H\rho$

3) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

4) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) none of these are correct

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ had

+a) constant magnitude over a portion of the Gaussian surface

-b) constant in direction over the entire Gaussian surface

-c) constant direction over a portion of the Gaussian surface

-d) constant direction and magnitude over the entire Gaussian surface

6) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, $dA_{1}=dA_{3}$

-a) True

+b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) none of these are correct

-c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-d) $2\varepsilon _{0}E=r\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

8) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-e) none of these are correct

Key: T0

1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) $\varepsilon _{0}E=H\rho z$

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=\rho z$

-e) none of these are correct

2) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho$

3) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) none of these are correct

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

4) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) none of these are correct

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

+a) $2r\varepsilon _{0}E=R^{2}\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) $2R\varepsilon _{0}E=r^{2}\rho$

-d) none of these are correct

-e) $2\varepsilon _{0}E=r\rho$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

8) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

Key: T1

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False

2) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=\rho z$

-b) none of these are correct

-c) $\varepsilon _{0}E=H\rho z$

-d) $\varepsilon _{0}E=H\rho$

+e) $\varepsilon _{0}E=H\rho /2$

4) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

+a) $\varepsilon _{0}E=\rho z$

-b) $\varepsilon _{0}E=H\rho$

-c) none of these are correct

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

6) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-b) $2R\varepsilon _{0}E=r^{2}\rho$

-c) none of these are correct

-d) $2\varepsilon _{0}E=r\rho$

+e) $2r\varepsilon _{0}E=R^{2}\rho$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

+b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

9) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

10) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) none of these are correct

+b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

Key: T2

1) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{3}\cdot dA_{3}=0$

-a) True

+b) False

2) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}+{\vec {E}}_{2}\cdot dA_{3}=0$

+a) True

-b) False

3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) $\varepsilon _{0}E=H\rho$

-b) none of these are correct

+c) $\varepsilon _{0}E=H\rho /2$

-d) $\varepsilon _{0}E=H\rho z$

-e) $\varepsilon _{0}E=\rho z$

4) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

-a) none of these are correct

+b) $\varepsilon _{0}E=\rho z$

-c) $\varepsilon _{0}E=H\rho$

-d) $\varepsilon _{0}E=H\rho /2$

-e) $\varepsilon _{0}E=H\rho z$

5) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated outside the Gaussian surface

-a) True

+b) False

6) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

-c) none of these are correct

-d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

+e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

7) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

-a) $2\varepsilon _{0}E=r\rho$

-b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$

-c) none of these are correct

+d) $2r\varepsilon _{0}E=R^{2}\rho$

-e) $2R\varepsilon _{0}E=r^{2}\rho$

8) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$

-b) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$

-c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$

-d) none of these are correct

+e) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$

9) If Gauss' law can be reduced to an algebraic expression that easily calculates the electric field $(\varepsilon _{0}EA^{*}=\rho V^{*})$, ${\vec {E}}$ was calculated on the Gaussian surface

+a) True

-b) False

10) In this description of the flux element, $d{\vec {S}}={\hat {n}}dA_{j}$ (j=1,2,3) where ${\hat {n}}$ is the outward unit normal, and a positive charge is assumed at point O, inside the Gaussian surface shown. The field lines exit at $S_{1}$ and $S_{3}$ but enter at $S_{2}$. In this figure, ${\vec {E}}_{1}\cdot dA_{1}={\vec {E}}_{3}\cdot dA_{3}$

+a) True

-b) False