# 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 ${\displaystyle \rho }$, 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

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

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

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

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

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

## C

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

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

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

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

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

## D

1 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

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

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

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

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

## E

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

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

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

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

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

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