A spherical conducting shell with zero net charge has an inner radius a and an outer radius b. A point charge q is placed at the center of the shell.

(a) Use Gauss's law and the properties of conductors in equilibrium to find the electric field in the regions r < a, a < r < b, and b < r.

(b) Draw the electric field lines for this situation.

(c) Find the charge density on the inner surface (r = a) and on the outer surface (r = b) of the shell.