Answer to Question #255445 in Electricity and Magnetism for Jer S

Question

A cuboid has a region of space that has constant charge density, p. Assume that the region is infinite in the x-y plane and of height d. Given that d is negligible, use Coulomb's law to find the electric field above and below the z-axis.

Answer 1

Inside.

$\oint EdA=\frac {q_{in}}{\epsilon _0},$

$dq=\rho dV=\rho xl^2dx,$

$q=\int dq=\frac{\rho l^2d^2}8,$

$E=\frac{\rho d^2}{8\epsilon _0}.$

Outside.

$\oint EdA=\frac{q_{in}}{\epsilon_0},$

$q=\int dq=\frac{\rho l^2a^2}{2},$

$E=\frac{\rho a^2}{2\epsilon_0}.$