Chapter 22, Problem 43P

(III) A very large (i.e., assume infinite) flat slab of nonconducting material has thickness d and a uniform volume charge density +ρ_E. (a) Show that a uniform electric field exists outside of this slab. Determine its magnitude E and its direction (relative to the slab’s surface). (b) As shown in Fig. 22–39, the slab is now aligned so that one of its surfaces lies on the line y = x. At time t = 0, a pointlike particle (mass m, charge +q) is located at position $\stackrel{\to }{r}=+y_0\hat{j}$ and has velocity $\stackrel{\to }{v}=v_0\hat{i}$. Show that the particle will collide with the slab if $v_0\ge \sqrt{\sqrt{2}q{y}_0{\rho }_{\text{E}}d/{\in }_{0}m}$. Ignore gravity.

FIGURE 22–39 Problem 43.