Question

in a region of space has constant charge density, p. Assume that the region is infinite in the x-y plane and of height, d. Determine the electric field inside and outside the charged region.

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.

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

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

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