Question

A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x=d and x=?d. The y- and z-dimensions of the slab are very large compared to d and may be treated as essentially infinite. Let the charge density of the slab be given by ?(x)=?0(x/d)2 where ?0 is a positive constant.

Part B

Using Gauss's law, find the magnitude of the electric field due to the slab at 0<|x|<d.

Express your answer in terms of the given quantities and constant ?0.

Answer 1

$\phi =2EA=Q_{inside}/\epsilon _{0}=2\rho Ax/\epsilon _{0}$

$So, E=\frac{\rho x}{\epsilon _{0}}=\frac{\rho _{0}}{2\epsilon _{0}d}x^{2}; -d\leq x\leq +d$