# 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 $\rho$ . 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?

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

 $\varepsilon _{0}E=H\rho /2$ b) none of these are correct c) $\varepsilon _{0}E=\rho z$ d) $\varepsilon _{0}E=H\rho$ e) $\varepsilon _{0}E=H\rho z$ 3 A sphere has a uniform charge density of $\rho$ , and a radius or R. What formula describes the electric field at a distance r > R?

 none of these are correct b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$ c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$ d) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$ e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$ 4 A sphere has a uniform charge density of $\rho$ , and a radius equal to R. What formula describes the electric field at a distance r < R?

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

 $2R\varepsilon _{0}E=r^{2}\rho$ b) $2r\varepsilon _{0}E=R^{2}\rho$ c) $2\varepsilon _{0}E=r\rho$ d) none of these are correct e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$ 6 A 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?

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