Chapter 22, Problem 22.49P

CALC An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by ρ(r) = α/r, where α is a positive constant. (a) In terms of α and a, what is the magnitude of the electric field at a distance r from the center of the shell, where a < r < b? (b) A point charge q is placed at the center of the hollow space, at r = 0. In terms of α and a, what value must q have (sign and magnitude) in order for the electric field to be constant in the region a < r < b, and what then is the value of the constant field in this region?