2. A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a "frozen-in" polarization P(r) == where k is a constant and r is the distance from the center. (There is no free charge in the problem.) Find the electric field in all three regions. (a) Locate all the bound charge, and use Gauss's law) to calculate the field it produces. (b) Use Eq. 4.23 to find D, and then get E from Eq. 4.21. [Notice that the second method is much faster, and it avoids any explicit reference to the bound charges.]