A solid, insulating sphere of radius $a$ has a uniform
charge density $\rho$ and a total charge $Q$ . Concentric with
this sphere is an uncharged, conducting, hollow sphere
whose inner and outer radii are $b$ and $c$ as shown in Figure $\mathrm{P} 24.47$ . (a) Find the magnitude of the electric field in
the regions $r<a, a<r<b, b<r<c,$ and $r>c$
(b) Determine the induced charge per unit area on the
inner and outer surfaces of the hollow sphere.