Chapter 22, Problem 47P

(III) A flat slab of nonconducting material has thickness 2d, which is small compared to its height and breadth. Define the x axis to be along the direction of the slab’s thickness with the origin at the center of the slab (Fig. 22–41). If the slab carries a volume charge density ρ_E (x) = −ρ₀ in the region −d ≤ x < 0 and ρ_E(x) = +ρ₀ in the region 0 < x ≤ +d, determine the electric field $\stackrel{\to }{E}$ as a function of x in the regions (a) outside the slab, (b) 0 < x ≤ + d, and (c) −d ≤ x < 0. Let ρ₀ be a positive constant.