Physics equations/19-Electric Potential and Electric Field/Q:UsingGaussLaw/testbank

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B

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

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

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

	a) $\varepsilon _{0}E=\rho z$
	b) $\varepsilon _{0}E=H\rho z$
	c) none of these are correct
	d) $\varepsilon _{0}E=H\rho /2$
	e) $\varepsilon _{0}E=H\rho$

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

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

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

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

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

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

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

	a) $\varepsilon _{0}E=H\rho z$
	b) $\varepsilon _{0}E=\rho z$
	c) none of these are correct
	d) $\varepsilon _{0}E=H\rho /2$
	e) $\varepsilon _{0}E=H\rho$

C

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

	a) $\varepsilon _{0}E=H\rho$
	b) $\varepsilon _{0}E=H\rho z$
	c) $\varepsilon _{0}E=H\rho /2$
	d) none of these are correct
	e) $\varepsilon _{0}E=\rho z$

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

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

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

	a) $\varepsilon _{0}E=H\rho /2$
	b) none of these are correct
	c) $\varepsilon _{0}E=H\rho$
	d) $\varepsilon _{0}E=\rho z$
	e) $\varepsilon _{0}E=H\rho z$

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

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

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

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

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

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

D

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

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

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

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

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

	a) $\varepsilon _{0}E=H\rho z$
	b) $\varepsilon _{0}E=H\rho$
	c) $\varepsilon _{0}E=H\rho /2$
	d) none of these are correct
	e) $\varepsilon _{0}E=\rho z$

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

	a) $\varepsilon _{0}E=H\rho /2$
	b) $\varepsilon _{0}E=H\rho z$
	c) $\varepsilon _{0}E=H\rho$
	d) none of these are correct
	e) $\varepsilon _{0}E=\rho z$

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

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

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

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

E

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

	a) $\varepsilon _{0}E=\rho z$
	b) $\varepsilon _{0}E=H\rho /2$
	c) none of these are correct
	d) $\varepsilon _{0}E=H\rho z$
	e) $\varepsilon _{0}E=H\rho$

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

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

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

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

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

	a) $\varepsilon _{0}E=H\rho /2$
	b) $\varepsilon _{0}E=H\rho$
	c) $\varepsilon _{0}E=\rho z$
	d) none of these are correct
	e) $\varepsilon _{0}E=H\rho z$

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

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

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

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