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A very long cylinder of linear dielectric material is

Chapter 4, Problem 22P

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QUESTION:

Problem 22P

A very long cylinder of linear dielectric material is placed in an otherwise uniform electric field E0. Find the resulting field within the cylinder. (The radius is a, the susceptibility χe, and the axis is perpendicular to E0.)

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QUESTION:

Problem 22P

A very long cylinder of linear dielectric material is placed in an otherwise uniform electric field E0. Find the resulting field within the cylinder. (The radius is a, the susceptibility χe, and the axis is perpendicular to E0.)

ANSWER:

Step 1 of 2


We have to find the resulting field within the cylinder due to an uniform electric field
.

The resulting field within the cylinder  can be found by solving Laplace’s equation for () and (under the boundary conditions.

Boundary condition (iii) implies that

     

Now condition (i) says,

 

whereas condition (ii) says,

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