Problem 4.15 A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a "frozen-in" polarization P(r) == f, where k is a constant and r is the distance from the center (Fig. 4.18). (There is no free charge in the problem.) Find the electric field in all three regions by two different methods: AP b P (a) Sphere (b) Needle (c) Wafer FIGURE 4.18 P FIGURE 4.19

Problem 4.15 A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a "frozen-in" polarization P(r) == f, where k is a constant and r is the distance from the center (Fig. 4.18). (There is no free charge in the problem.) Find the electric field in all three regions by two different methods: AP b P (a) Sphere (b) Needle (c) Wafer FIGURE 4.18 P FIGURE 4.19