and φ for a slab
A rectangular slab with uniform volume charge density ρ has thickness 2δ in the x direction and infinite extent in the y and z directions. Let the x coordinate be measured relative to the center plane of the slab. For values of x both inside and outside the slab:
(a) find the electric field E(x) (you can do this by considering the amount of charge on either side of x, or by using Gauss's law);
(b) find the potential φ(x), with φ taken to be zero at x = 0;
(c) verify that ρ(x) = ε₀ ∇ · E(x) and ρ(x) = -ε₀ ∇²φ(x).