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

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<quiz display=simple> {A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: Template:Nowrap. 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?} - ${\epsilon }_{0}E=\rho z$ -b) ${\epsilon }_{0}E=H\rho$ -c) ${\epsilon }_{0}E=H\rho z$ -d) none of these are correct +e) ${\epsilon }_{0}E=H\rho /2$

{A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much less than the radius: Template:Nowrap. 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?} - ${\epsilon }_{0}E=H\rho /2$ -b) none of these are correct +c) ${\epsilon }_{0}E=\rho z$ -d) ${\epsilon }_{0}E=H\rho$ -e) ${\epsilon }_{0}E=H\rho z$

{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) $r^2{\epsilon }_{0}E=R^3\rho /2$ -c) $r^2{\epsilon }_{0}E=r^3\rho /3$ -d) $r^2{\epsilon }_{0}E=r^3\rho /2$ +e) $r^2{\epsilon }_{0}E=R^3\rho /3$

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

{A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: Template:Nowrap. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R? } - $2R{\epsilon }_{0}E=r^2\rho$ -b) $2r{\epsilon }_{0}E=R^2\rho$ +c) $2{\epsilon }_{0}E=r\rho$ -d) none of these are correct -e) $2r^2{\epsilon }_{0}E=R^3\rho$

{A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: Template:Nowrap. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?} - $2R{\epsilon }_{0}E=r^2\rho$ -b) $2{\epsilon }_{0}E=r\rho$ +c) $2r{\epsilon }_{0}E=R^2\rho$ -d) none of these are correct -e) $2r^2{\epsilon }_{0}E=R^3\rho$ </quiz>