# Quizbank/University Physics Semester 2/T2

University Physics Semester 2/T2 ID153341821922

Exams:

78 Tests = 3 versions x 26 variations: Each of the 26 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.

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### T2 A0

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

a) 8.545E+01 V·m
b) 9.400E+01 V·m
c) 1.034E+02 V·m
d) 1.137E+02 V·m
e) 1.251E+02 V·m
2)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.777E+01 N·m2/C
b) 5.254E+01 N·m2/C
c) 5.780E+01 N·m2/C
d) 6.358E+01 N·m2/C
e) 6.993E+01 N·m2/C
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.125E+01 N·m2/C
b) 4.537E+01 N·m2/C
c) 4.991E+01 N·m2/C
d) 5.490E+01 N·m2/C
e) 6.039E+01 N·m2/C
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.1 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.606E+01 N·m2/C
b) 6.167E+01 N·m2/C
c) 6.784E+01 N·m2/C
d) 7.462E+01 N·m2/C
e) 8.208E+01 N·m2/C

5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 6.69E+03
b) 8.10E+03
c) 9.81E+03
d) 1.19E+04
e) 1.44E+04

6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.68z)\rho ^{2}{\hat {\rho }}+8.83z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 4.593E+03
b) 5.564E+03
c) 6.741E+03
d) 8.167E+03
e) 9.894E+03

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) none of these are correct

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
e) none of these are correct

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

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

a) none of these are correct
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

#### T2 A1

1) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
b) none of these are correct
c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
d) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
e) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) none of these are correct
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
c) none of these are correct
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.8 m, and z=z1=4.9 m. The surfaces in the yz plane each have area 8.1m2. Those in the xy plane have area 7.0m2 ,and those in the zx plane have area 8.4m2. An electric field has the xyz components (0, 9.2, 7.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.364E+01 N·m2/C
b) 7.000E+01 N·m2/C
c) 7.700E+01 N·m2/C
d) 8.470E+01 N·m2/C
e) 9.317E+01 N·m2/C

5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.93+2.31z)\rho ^{3}{\hat {\rho }}+7.21z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 5.40E+02
b) 6.55E+02
c) 7.93E+02
d) 9.61E+02
e) 1.16E+03

6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m
b) 2.871E+03 V·m
c) 3.158E+03 V·m
d) 3.474E+03 V·m
e) 3.822E+03 V·m

7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.68z)\rho ^{2}{\hat {\rho }}+8.83z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 4.593E+03
b) 5.564E+03
c) 6.741E+03
d) 8.167E+03
e) 9.894E+03

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) none of these are correct
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
9)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.1 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.606E+01 N·m2/C
b) 6.167E+01 N·m2/C
c) 6.784E+01 N·m2/C
d) 7.462E+01 N·m2/C
e) 8.208E+01 N·m2/C
10)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.439E+01 N·m2/C
b) 5.983E+01 N·m2/C
c) 6.581E+01 N·m2/C
d) 7.239E+01 N·m2/C
e) 7.963E+01 N·m2/C

#### T2 A2

1) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
b) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
c) none of these are correct
d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
e) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 6.201E+02
b) 7.513E+02
c) 9.102E+02
d) 1.103E+03
e) 1.336E+03
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.924E+01 N·m2/C
b) 4.316E+01 N·m2/C
c) 4.748E+01 N·m2/C
d) 5.222E+01 N·m2/C
e) 5.745E+01 N·m2/C

4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+1.11z)\rho ^{3}{\hat {\rho }}+8.16z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 4.69E+03
b) 5.69E+03
c) 6.89E+03
d) 8.35E+03
e) 1.01E+04

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
d) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
9)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.012E+01 N·m2/C
b) 2.213E+01 N·m2/C
c) 2.435E+01 N·m2/C
d) 2.678E+01 N·m2/C
e) 2.946E+01 N·m2/C
10)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.614E+01 N·m2/C
b) 7.275E+01 N·m2/C
c) 8.003E+01 N·m2/C
d) 8.803E+01 N·m2/C
e) 9.683E+01 N·m2/C

### T2 B0

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

a) 3.337E+03 V·m
b) 3.670E+03 V·m
c) 4.037E+03 V·m
d) 4.441E+03 V·m
e) 4.885E+03 V·m
2)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.876E+01 N·m2/C
b) 8.664E+01 N·m2/C
c) 9.531E+01 N·m2/C
d) 1.048E+02 N·m2/C
e) 1.153E+02 N·m2/C
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.662E+01 N·m2/C
b) 4.028E+01 N·m2/C
c) 4.430E+01 N·m2/C
d) 4.873E+01 N·m2/C
e) 5.361E+01 N·m2/C

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.383E+02 N/C
b) 1.522E+02 N/C
c) 1.674E+02 N/C
d) 1.841E+02 N/C
e) 2.025E+02 N/C

5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.44+2.86z)\rho ^{2}{\hat {\rho }}+7.42z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 9.41E+03
b) 1.14E+04
c) 1.38E+04
d) 1.67E+04
e) 2.03E+04

6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 4.489E+02
b) 5.438E+02
c) 6.589E+02
d) 7.983E+02
e) 9.671E+02

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho z}$
b) ${\displaystyle \varepsilon _{0}E=\rho z}$
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) none of these are correct
e) ${\displaystyle \varepsilon _{0}E=H\rho }$

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
c) none of these are correct
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
e) none of these are correct

#### T2 B1

1) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.04+1.66z)\rho ^{2}{\hat {\rho }}+7.54z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 8.528E+02
b) 1.033E+03
c) 1.252E+03
d) 1.516E+03
e) 1.837E+03

2) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=3 nC·m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?

a) 4.874E+01 N/C
b) 5.362E+01 N/C
c) 5.898E+01 N/C
d) 6.488E+01 N/C
e) 7.137E+01 N/C

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho z}$
b) ${\displaystyle \varepsilon _{0}E=\rho z}$
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) ${\displaystyle \varepsilon _{0}E=H\rho }$
e) none of these are correct
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.9 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 6.8m2 ,and those in the zx plane have area 7.7m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.898E+01 N·m2/C
b) 7.588E+01 N·m2/C
c) 8.347E+01 N·m2/C
d) 9.181E+01 N·m2/C
e) 1.010E+02 N·m2/C

5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

a) 3.429E+03 V·m
b) 3.771E+03 V·m
c) 4.149E+03 V·m
d) 4.564E+03 V·m
e) 5.020E+03 V·m

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
d) none of these are correct
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

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

a) none of these are correct
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
8)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.921E+01 N·m2/C
b) 9.813E+01 N·m2/C
c) 1.079E+02 N·m2/C
d) 1.187E+02 N·m2/C
e) 1.306E+02 N·m2/C

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) none of these are correct
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

10) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 4.63E+03
b) 5.61E+03
c) 6.79E+03
d) 8.23E+03
e) 9.97E+03

#### T2 B2

1)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.712E+01 N·m2/C
b) 4.083E+01 N·m2/C
c) 4.491E+01 N·m2/C
d) 4.940E+01 N·m2/C
e) 5.434E+01 N·m2/C

2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.89+1.31z)\rho ^{3}{\hat {\rho }}+8.35z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 9.41E+02
b) 1.14E+03
c) 1.38E+03
d) 1.67E+03
e) 2.03E+03

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

a) 2.210E+04 V·m
b) 2.431E+04 V·m
c) 2.674E+04 V·m
d) 2.941E+04 V·m
e) 3.235E+04 V·m

4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.93+2.31z)\rho ^{3}{\hat {\rho }}+7.21z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 6.731E+02
b) 8.154E+02
c) 9.879E+02
d) 1.197E+03
e) 1.450E+03

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) none of these are correct
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
b) none of these are correct
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) ${\displaystyle \varepsilon _{0}E=H\rho }$
e) ${\displaystyle \varepsilon _{0}E=H\rho z}$
7)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.737E+01 N·m2/C
b) 1.910E+01 N·m2/C
c) 2.101E+01 N·m2/C
d) 2.311E+01 N·m2/C
e) 2.543E+01 N·m2/C

8) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?

a) 2.039E+01 N/C
b) 2.243E+01 N/C
c) 2.467E+01 N/C
d) 2.714E+01 N/C
e) 2.985E+01 N/C

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

a) none of these are correct
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
e) none of these are correct

### T2 C0

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

a) 2.067E+03 V·m
b) 2.274E+03 V·m
c) 2.501E+03 V·m
d) 2.752E+03 V·m
e) 3.027E+03 V·m
2)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 9.823E+00 N·m2/C
b) 1.080E+01 N·m2/C
c) 1.189E+01 N·m2/C
d) 1.307E+01 N·m2/C
e) 1.438E+01 N·m2/C
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.614E+01 N·m2/C
b) 7.275E+01 N·m2/C
c) 8.003E+01 N·m2/C
d) 8.803E+01 N·m2/C
e) 9.683E+01 N·m2/C

4) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

a) 3.821E+02 N/C
b) 4.203E+02 N/C
c) 4.624E+02 N/C
d) 5.086E+02 N/C
e) 5.594E+02 N/C

5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.45+2.26z)\rho ^{2}{\hat {\rho }}+8.92z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 1.29E+03
b) 1.56E+03
c) 1.89E+03
d) 2.29E+03
e) 2.77E+03

6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.45+2.26z)\rho ^{2}{\hat {\rho }}+8.92z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 5.043E+02
b) 6.109E+02
c) 7.402E+02
d) 8.967E+02
e) 1.086E+03

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
b) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
c) none of these are correct
d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=\rho z}$
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) ${\displaystyle \varepsilon _{0}E=H\rho }$
e) ${\displaystyle \varepsilon _{0}E=H\rho z}$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) none of these are correct
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) none of these are correct

#### T2 C1

1)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.662E+01 N·m2/C
b) 4.028E+01 N·m2/C
c) 4.430E+01 N·m2/C
d) 4.873E+01 N·m2/C
e) 5.361E+01 N·m2/C

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
b) none of these are correct
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

3) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C
b) 2.501E+02 N/C
c) 2.751E+02 N/C
d) 3.026E+02 N/C
e) 3.329E+02 N/C

4) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
b) ${\displaystyle \varepsilon _{0}E=H\rho z}$
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) none of these are correct
e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.07+2.87z)\rho ^{2}{\hat {\rho }}+9.56z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 1.59E+03
b) 1.93E+03
c) 2.34E+03
d) 2.83E+03
e) 3.43E+03

6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.9}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.5}{\hat {k}}}$

a) 4.286E+03 V·m
b) 4.714E+03 V·m
c) 5.186E+03 V·m
d) 5.704E+03 V·m
e) 6.275E+03 V·m

7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.68z)\rho ^{2}{\hat {\rho }}+8.83z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 4.593E+03
b) 5.564E+03
c) 6.741E+03
d) 8.167E+03
e) 9.894E+03

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
c) none of these are correct
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
9)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.074E+01 N·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

#### T2 C2

1)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.662E+01 N·m2/C
b) 4.028E+01 N·m2/C
c) 4.430E+01 N·m2/C
d) 4.873E+01 N·m2/C
e) 5.361E+01 N·m2/C

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) none of these are correct
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

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

a) none of these are correct
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
5)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.978E+01 N·m2/C
b) 6.576E+01 N·m2/C
c) 7.233E+01 N·m2/C
d) 7.957E+01 N·m2/C
e) 8.752E+01 N·m2/C

6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 1.09E+03
b) 1.32E+03
c) 1.60E+03
d) 1.94E+03
e) 2.35E+03

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

a) 8.545E+01 V·m
b) 9.400E+01 V·m
c) 1.034E+02 V·m
d) 1.137E+02 V·m
e) 1.251E+02 V·m

8) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C
b) 2.501E+02 N/C
c) 2.751E+02 N/C
d) 3.026E+02 N/C
e) 3.329E+02 N/C

9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.45+2.26z)\rho ^{2}{\hat {\rho }}+8.92z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 5.043E+02
b) 6.109E+02
c) 7.402E+02
d) 8.967E+02
e) 1.086E+03

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
c) ${\displaystyle \varepsilon _{0}E=H\rho }$
d) ${\displaystyle \varepsilon _{0}E=\rho z}$
e) none of these are correct

### T2 D0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

a) 3.251E+01 N/C
b) 3.577E+01 N/C
c) 3.934E+01 N/C
d) 4.328E+01 N/C
e) 4.760E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m
b) 7.759E+03 V·m
c) 8.535E+03 V·m
d) 9.388E+03 V·m
e) 1.033E+04 V·m
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.756E+01 N·m2/C
b) 3.032E+01 N·m2/C
c) 3.335E+01 N·m2/C
d) 3.668E+01 N·m2/C
e) 4.035E+01 N·m2/C
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 5.3m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.793E+01 N·m2/C
b) 8.572E+01 N·m2/C
c) 9.429E+01 N·m2/C
d) 1.037E+02 N·m2/C
e) 1.141E+02 N·m2/C

5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 4.489E+02
b) 5.438E+02
c) 6.589E+02
d) 7.983E+02
e) 9.671E+02

6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+1.11z)\rho ^{3}{\hat {\rho }}+8.16z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 9.205E+02
b) 1.115E+03
c) 1.351E+03
d) 1.637E+03
e) 1.983E+03

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) none of these are correct

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
b) ${\displaystyle \varepsilon _{0}E=\rho z}$
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) ${\displaystyle \varepsilon _{0}E=H\rho z}$
e) none of these are correct

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) none of these are correct

#### T2 D1

1) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
b) ${\displaystyle \varepsilon _{0}E=H\rho z}$
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) none of these are correct
e) ${\displaystyle \varepsilon _{0}E=H\rho }$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
b) none of these are correct
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

3) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 5.610E+02
b) 6.796E+02
c) 8.234E+02
d) 9.975E+02
e) 1.209E+03
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.5 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 8.3m2. Those in the xy plane have area 5.7m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.408E+01 N·m2/C
b) 5.949E+01 N·m2/C
c) 6.544E+01 N·m2/C
d) 7.198E+01 N·m2/C
e) 7.918E+01 N·m2/C

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) none of these are correct
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+2.08z)\rho ^{2}{\hat {\rho }}+8.93z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 1.704E+03
b) 2.064E+03
c) 2.501E+03
d) 3.030E+03
e) 3.671E+03

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
e) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
8)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.186E+01 N·m2/C
b) 2.404E+01 N·m2/C
c) 2.645E+01 N·m2/C
d) 2.909E+01 N·m2/C
e) 3.200E+01 N·m2/C

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

a) 2.837E+01 N/C
b) 3.121E+01 N/C
c) 3.433E+01 N/C
d) 3.776E+01 N/C
e) 4.154E+01 N/C

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

a) 1.997E+03 V·m
b) 2.197E+03 V·m
c) 2.417E+03 V·m
d) 2.659E+03 V·m
e) 2.924E+03 V·m

#### T2 D2

1) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) none of these are correct
d) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
e) ${\displaystyle \varepsilon _{0}E=H\rho z}$

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

a) none of these are correct
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

3) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.04+1.66z)\rho ^{2}{\hat {\rho }}+7.54z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 8.528E+02
b) 1.033E+03
c) 1.252E+03
d) 1.516E+03
e) 1.837E+03

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?

a) 9.642E+00 N/C
b) 1.061E+01 N/C
c) 1.167E+01 N/C
d) 1.283E+01 N/C
e) 1.412E+01 N/C

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) none of these are correct
c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2+1.45z)\rho ^{2}{\hat {\rho }}+8.02z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 4.021E+02
b) 4.872E+02
c) 5.902E+02
d) 7.151E+02
e) 8.663E+02
7)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.921E+01 N·m2/C
b) 9.813E+01 N·m2/C
c) 1.079E+02 N·m2/C
d) 1.187E+02 N·m2/C
e) 1.306E+02 N·m2/C

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) none of these are correct
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
9)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.924E+01 N·m2/C
b) 4.316E+01 N·m2/C
c) 4.748E+01 N·m2/C
d) 5.222E+01 N·m2/C
e) 5.745E+01 N·m2/C

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{1.4}{\hat {i}}+2x^{2.3}{\hat {j}}+4y^{2.3}{\hat {k}}}$

a) 2.694E+03 V·m
b) 2.963E+03 V·m
c) 3.259E+03 V·m
d) 3.585E+03 V·m
e) 3.944E+03 V·m

### T2 E0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?

a) 8.580E+00 N/C
b) 9.438E+00 N/C
c) 1.038E+01 N/C
d) 1.142E+01 N/C
e) 1.256E+01 N/C
2)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.876E+01 N·m2/C
b) 8.664E+01 N·m2/C
c) 9.531E+01 N·m2/C
d) 1.048E+02 N·m2/C
e) 1.153E+02 N·m2/C
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.737E+01 N·m2/C
b) 1.910E+01 N·m2/C
c) 2.101E+01 N·m2/C
d) 2.311E+01 N·m2/C
e) 2.543E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}}$

a) 1.206E+03 V·m
b) 1.326E+03 V·m
c) 1.459E+03 V·m
d) 1.605E+03 V·m
e) 1.765E+03 V·m

5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.17+1.5z)\rho ^{2}{\hat {\rho }}+8.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 2.454E+02
b) 2.973E+02
c) 3.601E+02
d) 4.363E+02
e) 5.286E+02

6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 6.69E+03
b) 8.10E+03
c) 9.81E+03
d) 1.19E+04
e) 1.44E+04

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

a) none of these are correct
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) none of these are correct
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) none of these are correct
e) ${\displaystyle \varepsilon _{0}E=H\rho z}$

#### T2 E1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?

a) 9.592E+00 N/C
b) 1.055E+01 N/C
c) 1.161E+01 N/C
d) 1.277E+01 N/C
e) 1.404E+01 N/C

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
b) none of these are correct
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=\rho z}$
b) none of these are correct
c) ${\displaystyle \varepsilon _{0}E=H\rho }$
d) ${\displaystyle \varepsilon _{0}E=H\rho z}$
e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
5)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.992E+01 N·m2/C
b) 2.192E+01 N·m2/C
c) 2.411E+01 N·m2/C
d) 2.652E+01 N·m2/C
e) 2.917E+01 N·m2/C

6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2+1.45z)\rho ^{2}{\hat {\rho }}+8.02z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 1.13E+03
b) 1.37E+03
c) 1.66E+03
d) 2.01E+03
e) 2.44E+03
7)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 9.823E+00 N·m2/C
b) 1.080E+01 N·m2/C
c) 1.189E+01 N·m2/C
d) 1.307E+01 N·m2/C
e) 1.438E+01 N·m2/C

8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 5.610E+02
b) 6.796E+02
c) 8.234E+02
d) 9.975E+02
e) 1.209E+03

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) none of these are correct
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
b) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
e) none of these are correct

#### T2 E2

1) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.07+2.87z)\rho ^{2}{\hat {\rho }}+9.56z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 4.162E+02
b) 5.042E+02
c) 6.109E+02
d) 7.401E+02
e) 8.967E+02

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) none of these are correct
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m
b) 2.871E+03 V·m
c) 3.158E+03 V·m
d) 3.474E+03 V·m
e) 3.822E+03 V·m
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.6m2 ,and those in the zx plane have area 13.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 46° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.988E+01 N·m2/C
b) 5.487E+01 N·m2/C
c) 6.035E+01 N·m2/C
d) 6.639E+01 N·m2/C
e) 7.303E+01 N·m2/C

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
c) none of these are correct
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) none of these are correct
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.88+1.29z)\rho ^{2}{\hat {\rho }}+7.2z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 1.08E+03
b) 1.30E+03
c) 1.58E+03
d) 1.91E+03
e) 2.32E+03

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho z}$
c) none of these are correct
d) ${\displaystyle \varepsilon _{0}E=H\rho }$
e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.5 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

a) 2.601E+01 N/C
b) 2.861E+01 N/C
c) 3.147E+01 N/C
d) 3.462E+01 N/C
e) 3.808E+01 N/C
10)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.385E+01 N·m2/C
b) 5.923E+01 N·m2/C
c) 6.516E+01 N·m2/C
d) 7.167E+01 N·m2/C
e) 7.884E+01 N·m2/C

### T2 F0

1)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.8 m, and z=z1=4.9 m. The surfaces in the yz plane each have area 8.1m2. Those in the xy plane have area 7.0m2 ,and those in the zx plane have area 8.4m2. An electric field has the xyz components (0, 9.2, 7.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.364E+01 N·m2/C
b) 7.000E+01 N·m2/C
c) 7.700E+01 N·m2/C
d) 8.470E+01 N·m2/C
e) 9.317E+01 N·m2/C

2) A non-conducting sphere of radius R=1.4 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.6 (r≤R) where a=3 nC·m-1.4. What is the magnitude of the electric field at a distance of 1.3 m from the center?

a) 1.457E+02 N/C
b) 1.603E+02 N/C
c) 1.763E+02 N/C
d) 1.939E+02 N/C
e) 2.133E+02 N/C
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.134E+01 N·m2/C
b) 2.347E+01 N·m2/C
c) 2.582E+01 N·m2/C
d) 2.840E+01 N·m2/C
e) 3.124E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m
b) 7.759E+03 V·m
c) 8.535E+03 V·m
d) 9.388E+03 V·m
e) 1.033E+04 V·m

5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 1.09E+03
b) 1.32E+03
c) 1.60E+03
d) 1.94E+03
e) 2.35E+03

6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 5.610E+02
b) 6.796E+02
c) 8.234E+02
d) 9.975E+02
e) 1.209E+03

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
b) ${\displaystyle \varepsilon _{0}E=H\rho z}$
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
e) none of these are correct

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) none of these are correct
d) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
e) ${\displaystyle \varepsilon _{0}E=\rho z}$

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
b) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) none of these are correct
e) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) none of these are correct
e) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

#### T2 F1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

a) 2.210E+04 V·m
b) 2.431E+04 V·m
c) 2.674E+04 V·m
d) 2.941E+04 V·m
e) 3.235E+04 V·m

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
e) none of these are correct
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.978E+01 N·m2/C
b) 6.576E+01 N·m2/C
c) 7.233E+01 N·m2/C
d) 7.957E+01 N·m2/C
e) 8.752E+01 N·m2/C

4) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
b) none of these are correct
c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
5)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.737E+01 N·m2/C
b) 1.910E+01 N·m2/C
c) 2.101E+01 N·m2/C
d) 2.311E+01 N·m2/C
e) 2.543E+01 N·m2/C

6) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C

7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.89+1.31z)\rho ^{3}{\hat {\rho }}+8.35z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 9.41E+02
b) 1.14E+03
c) 1.38E+03
d) 1.67E+03
e) 2.03E+03

8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.96+2.52z)\rho ^{2}{\hat {\rho }}+7.11z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 4.027E+02
b) 4.879E+02
c) 5.911E+02
d) 7.162E+02
e) 8.676E+02

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=\rho z}$
b) none of these are correct
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) ${\displaystyle \varepsilon _{0}E=H\rho z}$
e) ${\displaystyle \varepsilon _{0}E=H\rho }$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
b) none of these are correct
c) ${\displaystyle \varepsilon _{0}E=H\rho z}$
d) ${\displaystyle \varepsilon _{0}E=\rho z}$
e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

#### T2 F2

1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+2.08z)\rho ^{2}{\hat {\rho }}+8.93z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 3.13E+03
b) 3.79E+03
c) 4.59E+03
d) 5.56E+03
e) 6.74E+03

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
e) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
b) none of these are correct
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) ${\displaystyle \varepsilon _{0}E=H\rho }$
e) ${\displaystyle \varepsilon _{0}E=H\rho z}$
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.074E+01 N·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) ${\displaystyle \varepsilon _{0}E=H\rho z}$
d) none of these are correct
e) ${\displaystyle \varepsilon _{0}E=\rho z}$

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
b) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) none of these are correct
7)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.270E+01 N·m2/C
b) 6.897E+01 N·m2/C
c) 7.586E+01 N·m2/C
d) 8.345E+01 N·m2/C
e) 9.179E+01 N·m2/C

8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.9}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.5}{\hat {k}}}$

a) 4.286E+03 V·m
b) 4.714E+03 V·m
c) 5.186E+03 V·m
d) 5.704E+03 V·m
e) 6.275E+03 V·m

9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.07+2.87z)\rho ^{2}{\hat {\rho }}+9.56z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 4.162E+02
b) 5.042E+02
c) 6.109E+02
d) 7.401E+02
e) 8.967E+02

10) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.123E+02 N/C
b) 1.235E+02 N/C
c) 1.358E+02 N/C
d) 1.494E+02 N/C
e) 1.644E+02 N/C

### T2 G0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?

a) 1.017E+01 N/C
b) 1.118E+01 N/C
c) 1.230E+01 N/C
d) 1.353E+01 N/C
e) 1.488E+01 N/C
2)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.662E+01 N·m2/C
b) 4.028E+01 N·m2/C
c) 4.430E+01 N·m2/C
d) 4.873E+01 N·m2/C
e) 5.361E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.3}{\hat {i}}+3x^{2.4}{\hat {j}}+2y^{1.8}{\hat {k}}}$

a) 8.731E+02 V·m
b) 9.604E+02 V·m
c) 1.056E+03 V·m
d) 1.162E+03 V·m
e) 1.278E+03 V·m
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.891E+01 N·m2/C
b) 2.080E+01 N·m2/C
c) 2.288E+01 N·m2/C
d) 2.517E+01 N·m2/C
e) 2.768E+01 N·m2/C

5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.07+2.87z)\rho ^{2}{\hat {\rho }}+9.56z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 1.59E+03
b) 1.93E+03
c) 2.34E+03
d) 2.83E+03
e) 3.43E+03

6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+1.11z)\rho ^{3}{\hat {\rho }}+8.16z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 2.769E+03
b) 3.354E+03
c) 4.064E+03
d) 4.923E+03
e) 5.965E+03

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
b) ${\displaystyle \varepsilon _{0}E=H\rho z}$
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) ${\displaystyle \varepsilon _{0}E=\rho z}$
e) none of these are correct

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) ${\displaystyle \varepsilon _{0}E=H\rho z}$
e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
c) none of these are correct
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

#### T2 G1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.9}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.5}{\hat {k}}}$

a) 4.286E+03 V·m
b) 4.714E+03 V·m
c) 5.186E+03 V·m
d) 5.704E+03 V·m
e) 6.275E+03 V·m
2)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.2 m, z=z0=1.9 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 8.1m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 8.5, 6.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.081E+01 N·m2/C
b) 7.789E+01 N·m2/C
c) 8.568E+01 N·m2/C
d) 9.425E+01 N·m2/C
e) 1.037E+02 N·m2/C

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) none of these are correct
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
4)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.270E+01 N·m2/C
b) 6.897E+01 N·m2/C
c) 7.586E+01 N·m2/C
d) 8.345E+01 N·m2/C
e) 9.179E+01 N·m2/C

5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 6.69E+03
b) 8.10E+03
c) 9.81E+03
d) 1.19E+04
e) 1.44E+04

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
b) ${\displaystyle \varepsilon _{0}E=H\rho z}$
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
e) none of these are correct

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
b) ${\displaystyle \varepsilon _{0}E=\rho z}$
c) none of these are correct
d) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
e) ${\displaystyle \varepsilon _{0}E=H\rho z}$

8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 3.417E+03
b) 4.140E+03
c) 5.016E+03
d) 6.077E+03
e) 7.362E+03

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

a) 2.837E+01 N/C
b) 3.121E+01 N/C
c) 3.433E+01 N/C
d) 3.776E+01 N/C
e) 4.154E+01 N/C

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
c) none of these are correct
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

#### T2 G2

1) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 1.362E+03
b) 1.650E+03
c) 2.000E+03
d) 2.423E+03
e) 2.935E+03

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?

a) 6.641E+00 N/C
b) 7.305E+00 N/C
c) 8.036E+00 N/C
d) 8.839E+00 N/C
e) 9.723E+00 N/C

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

4) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
c) none of these are correct
d) ${\displaystyle \varepsilon _{0}E=\rho z}$
e) ${\displaystyle \varepsilon _{0}E=H\rho }$

5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2+1.45z)\rho ^{2}{\hat {\rho }}+8.02z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 1.13E+03
b) 1.37E+03
c) 1.66E+03
d) 2.01E+03
e) 2.44E+03

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
c) none of these are correct
d) ${\displaystyle \varepsilon _{0}E=\rho z}$
e) ${\displaystyle \varepsilon _{0}E=H\rho }$

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.0}{\hat {i}}+3x^{2.0}{\hat {j}}+3y^{3.0}{\hat {k}}}$

a) 4.820E+03 V·m
b) 5.302E+03 V·m
c) 5.832E+03 V·m
d) 6.415E+03 V·m
e) 7.057E+03 V·m
8)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 13.0m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 7.0, 5.7) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.953E+01 N·m2/C
b) 5.449E+01 N·m2/C
c) 5.993E+01 N·m2/C
d) 6.593E+01 N·m2/C
e) 7.252E+01 N·m2/C
9)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.921E+01 N·m2/C
b) 9.813E+01 N·m2/C
c) 1.079E+02 N·m2/C
d) 1.187E+02 N·m2/C
e) 1.306E+02 N·m2/C

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
b) none of these are correct
c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

### T2 H0

1) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C
2)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.0 m, z=z0=1.9 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.9m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 2.9m2. An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.388E+01 N·m2/C
b) 1.526E+01 N·m2/C
c) 1.679E+01 N·m2/C
d) 1.847E+01 N·m2/C
e) 2.032E+01 N·m2/C
3)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.186E+01 N·m2/C
b) 2.404E+01 N·m2/C
c) 2.645E+01 N·m2/C
d) 2.909E+01 N·m2/C
e) 3.200E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

a) 3.429E+03 V·m
b) 3.771E+03 V·m
c) 4.149E+03 V·m
d) 4.564E+03 V·m
e) 5.020E+03 V·m

5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.17+1.5z)\rho ^{2}{\hat {\rho }}+8.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 3.630E+02
b) 4.398E+02
c) 5.329E+02
d) 6.456E+02
e) 7.821E+02

6) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 7.465E+02
b) 9.044E+02
c) 1.096E+03
d) 1.327E+03
e) 1.608E+03

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) none of these are correct

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) none of these are correct
e) ${\displaystyle \varepsilon _{0}E=\rho z}$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) none of these are correct
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

#### T2 H1

1) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?

a) 2.039E+01 N/C
b) 2.243E+01 N/C
c) 2.467E+01 N/C
d) 2.714E+01 N/C
e) 2.985E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}}$

a) 1.206E+03 V·m
b) 1.326E+03 V·m
c) 1.459E+03 V·m
d) 1.605E+03 V·m
e) 1.765E+03 V·m

3) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.04+1.66z)\rho ^{2}{\hat {\rho }}+7.54z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 9.431E+02
b) 1.143E+03
c) 1.384E+03
d) 1.677E+03
e) 2.032E+03

4) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho }$
b) ${\displaystyle \varepsilon _{0}E=\rho z}$
c) none of these are correct
d) ${\displaystyle \varepsilon _{0}E=H\rho z}$
e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
c) none of these are correct
d) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
6)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.992E+01 N·m2/C
b) 2.192E+01 N·m2/C
c) 2.411E+01 N·m2/C
d) 2.652E+01 N·m2/C
e) 2.917E+01 N·m2/C
7)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.2 m, z=z0=1.9 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 8.1m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 8.5, 6.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.081E+01 N·m2/C
b) 7.789E+01 N·m2/C
c) 8.568E+01 N·m2/C
d) 9.425E+01 N·m2/C
e) 1.037E+02 N·m2/C

8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.68z)\rho ^{2}{\hat {\rho }}+8.83z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 4.593E+03
b) 5.564E+03
c) 6.741E+03
d) 8.167E+03
e) 9.894E+03

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

a) none of these are correct
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) none of these are correct
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

#### T2 H2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{1.4}{\hat {i}}+2x^{2.3}{\hat {j}}+4y^{2.3}{\hat {k}}}$

a) 2.694E+03 V·m
b) 2.963E+03 V·m
c) 3.259E+03 V·m
d) 3.585E+03 V·m
e) 3.944E+03 V·m

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) none of these are correct
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

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

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.14+2.8z)\rho ^{2}{\hat {\rho }}+9.94z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 2.420E+02
b) 2.931E+02
c) 3.551E+02
d) 4.303E+02
e) 5.213E+02

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
d) none of these are correct
e) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.17+1.5z)\rho ^{2}{\hat {\rho }}+8.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 3.630E+02
b) 4.398E+02
c) 5.329E+02
d) 6.456E+02
e) 7.821E+02
7)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.901E+01 N·m2/C
b) 3.192E+01 N·m2/C
c) 3.511E+01 N·m2/C
d) 3.862E+01 N·m2/C
e) 4.248E+01 N·m2/C

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. 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) ${\displaystyle \varepsilon _{0}E=H\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) ${\displaystyle \varepsilon _{0}E=\rho z}$
d) none of these are correct
e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

9) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C
10)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=4.2 m, z=z0=1.2 m, and z=z1=4.1 m. The surfaces in the yz plane each have area 8.7m2. Those in the xy plane have area 7.2m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.024E+01 N·m2/C
b) 4.426E+01 N·m2/C
c) 4.868E+01 N·m2/C
d) 5.355E+01 N·m2/C
e) 5.891E+01 N·m2/C

### T2 I0

1)
Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.698E+01 N·m2/C
b) 1.868E+01 N·m2/C
c) 2.055E+01 N·m2/C
d) 2.260E+01 N·m2/C
e) 2.486E+01 N·m2/C

2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?

a) 2.039E+01 N/C
b) 2.243E+01 N/C
c) 2.467E+01 N/C
d) 2.714E+01 N/C
e) 2.985E+01 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?

a) 9.592E+00 N/C
b) 1.055E+01 N/C
c) 1.161E+01 N/C
d) 1.277E+01 N/C
e) 1.404E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with