Chapter 22, Problem 22.44P

A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is −3Q, and it is insulated from its surroundings (Fig. P22.44). (a) Derive expressions for the electric-field magnitude E in terms of the distance r from the center for the regions r < a, a < r < b, and r > b. What is the surface charge density (b) on the inner surface of the conducting shell; (c) on the outer surface of the conducting shell? (d) Sketch the electric field lines and the | location of all charges, (e) Graph E as a function of r.

Figure P22.44