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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 clectric field in all three regions by two different methods: (a) Locate all the bound charge, and use Gauss's law (Eq. 2.13) 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 avoids any explicit reference to the bound charges.] Figure 4.18 For any closed surface, then, E- da = Qene. (2.13) D = €qE + P, (4.21) da = Q fen " (4.23)

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 clectric field in all three regions by two different methods: (a) Locate all the bound charge, and use Gauss's law (Eq. 2.13) 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 avoids any explicit reference to the bound charges.] Figure 4.18 For any closed surface, then, E- da = Qene. (2.13) D = €qE + P, (4.21) da = Q fen " (4.23)

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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: (a) Locate all the bound charge, and use Gauss's law (Eq. 2.13) 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 avoids any explicit reference to the bound charges.) Figure 4.18 For any closed surface, then, E da = Qenc- (2.13) €0 D = €0E + P, (4.21) da = Q fec (4.23)
Transcribed Image Text: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: (a) Locate all the bound charge, and use Gauss's law (Eq. 2.13) 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 avoids any explicit reference to the bound charges.) Figure 4.18 For any closed surface, then, E da = Qenc- (2.13) €0 D = €0E + P, (4.21) da = Q fec (4.23)
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