Suppose the field inside a large piece of dielectric is E0, so that the electric displac...

Suppose the field inside a large piece of dielectric is E0, so that the electric displacement is

(a) Now a small spherical cavity (Fig. 4.19a) is hollowed out of the material. Find the field at the center of the cavity in terms of E₀ and P. Also find the displacement at the center of the cavity in terms of D₀ and P. Assume the polarization is “frozen in,” so it doesn’t change when the cavity is excavated.

(b) Do the same for a long needle-shaped cavity running parallel to P (Fig. 4.19b).

(c) Do the same for a thin wafer-shaped cavity perpendicular to P (Fig. 4.19c). Assume the cavities are small enough that P, E₀, and D₀ are essentially uniform. [Hint: Carving out a cavity is the same as superimposing an object of the same shape but opposite polarization.]

Figure 4.19