Question

A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a "frozen-in" polarization P?(r?) = k/r r? 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: (a) Locate all the bound charge, and use Gauss's law to calculate the field it produces. (b) Use ? D? ? da? = Q_{f,enc} to find D, and then get E from D? = ??E? + P?. [Notice that the second method is much faster, and it avoids any explicit reference to the bound charges.]

          A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a "frozen-in" polarization

P?(r?) = k/r r?

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:

(a) Locate all the bound charge, and use Gauss's law to calculate the field it produces.
(b) Use ? D? ? da? = Q_{f,enc} to find D, and then get E from D? = ??E? + P?. [Notice that the second method is much faster, and it avoids any explicit reference to the bound charges.]

A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a "frozen-in" polarization

P?(r?) = k/r r?

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:

(a) Locate all the bound charge, and use Gauss's law to calculate the field it produces.
(b) Use ? D? ? da? = Qf,enc to find D, and then get E from D? = ??E? + P?. [Notice that the second method is much faster, and it avoids any explicit reference to the bound charges.]

Added by Evan P.

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