Chapter 22, Problem 22.48P

A solid conducting sphere with radius R carries a positive total charge Q. The sphere is surrounded by an insulating shell with inner radius R and outer radius 2R. The insulating shell has a uniform charge density ρ. (a) Find the value of ρ so that the net charge of the entire system is zero. (b) If ρ has the value found in part (a), find the electric field $\stackrel{\to }{\text{E}}$ (magnitude and direction) in each of the regions 0 < r < R, R < r < 2R, and r > 2R. Graph the radial component of $\stackrel{\to }{\text{E}}$ as a function of r. (c) As a general rule, the electric field is discontinuous only at locations where there is a thin sheet of charge. Explain how your results in part (b) agree with this rule.