Chapter 22 Problem 60

Problem

Interface effects

A very large thin plane has uniform surface charge density $\sigma$.Touching it on the right is a long wide slab of thickness d with uniform volume charge density $\rho _{E}$. Determine the electric field

(a) to the left of the plane,

(b) to the right of the slab, and

(c) everywhere inside the slab.

Solution

The field due to the plane is --- (as discussed in the lesson). Because the slab is very large, and we assume that we are considering only distances from the slab much less than its height or breadth, the symmetry of the slab results in its field being perpendicular to the slab, with a constant magnitude for a constant distance from its center. We also assume that --- and so the electric field of the slab points away from the center of the slab.