Chapter 21, Problem 75P

Repeal Problem 59 for the case where the charge density in the slab is given by ρ = ρ₀|x/d|, where ρ₀ is a constant.

59. A charged slab extends infinitely in two dimensions and has thickness d in the third dimension, as shown in Fig. 21.36. The slab carries a uniform volume charge density ρ. Find expressions for the electric field (a) inside and (b) outside the slab, as functions of the distance x from the center plane. (Although the infinite slab is impossible, your answer is a good approximation to the field of a finite slab whose width is much greater than its thickness.)

  

FIGURE 21.36 Problems 59 and 75