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 p.
(a) Find the value of p so that the net charge of the entire system is zero.
(b) If p has the value found in part (a), find the electric field (magnitude and direction) in each of the regions 0 < r < R, R < r < 2R, and r > 2R. Show your results in a graph of the radial component of 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.