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Find the field inside a sphere of linear dielectric
Chapter 4, Problem 23P(choose chapter or problem)
Problem 23P
Find the field inside a sphere of linear dielectric material in an otherwise uniform electric field E0 (Ex. 4.7) by the following method of successive approximations: First pretend the field inside is just E0, and use Eq. 4.30 to write down the resulting polarization P0. This polarization generates a field of its own, E1 (Ex. 4.2), which in turn modifies the polarization by an amount P1, which further changes the field by an amount E2, and so on. The resulting field is E0 + E1+ E2 +· · · . Sum the series, and compare your answer with Eq. 4.49.
REFERENCE EX. 4.7 A sphere of homogeneous linear dielectric material is placed in an otherwise uniform electric field E0 (Fig.4.27). Find the electric field inside the sphere.
REFERENCE EXAMPLE 4.2 Find the electric field produced by a uniformly polarized sphere of radius R.
Reference equation 4.30
Reference equation 4.49
Questions & Answers
QUESTION:
Problem 23P
Find the field inside a sphere of linear dielectric material in an otherwise uniform electric field E0 (Ex. 4.7) by the following method of successive approximations: First pretend the field inside is just E0, and use Eq. 4.30 to write down the resulting polarization P0. This polarization generates a field of its own, E1 (Ex. 4.2), which in turn modifies the polarization by an amount P1, which further changes the field by an amount E2, and so on. The resulting field is E0 + E1+ E2 +· · · . Sum the series, and compare your answer with Eq. 4.49.
REFERENCE EX. 4.7 A sphere of homogeneous linear dielectric material is placed in an otherwise uniform electric field E0 (Fig.4.27). Find the electric field inside the sphere.
REFERENCE EXAMPLE 4.2 Find the electric field produced by a uniformly polarized sphere of radius R.
Reference equation 4.30
Reference equation 4.49
ANSWER:Step 1 of 3
We have to find the electric field inside a sphere of dielectric medium by the method of successive approximations.
Firstly, the field inside the sphere is just and the resulting polarization due to this is given by the expression,
Now, this polarization generates a field of its own which modifies the polarization by and the field can be written using the expression,
Substituting for ,
So, the polarization due to this electric field is,
Substituting for ,