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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b6d687b-9b3f-47af-8b4d-c251df44093c%2F9f38a6eb-3a74-440c-aef8-b0bf10e271bd%2Fil867mk_processed.png&w=3840&q=75)
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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