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

A

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?

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

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?

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

3 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?

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

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?

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

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?

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

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?

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