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## Homework Statement

A dielectric sphere of radius R has a uniform permanent polarisation

**P**. Determine the electric field both inside and outside the sphere. (Hint: Since div

**P**= 0 everywhere, the electrostatic potential satisfies Laplace's equation. Do not assume that the sphere is characterised by a dielectric constant. Instead, use

**D**= [tex]\epsilon_{0}[/tex]

**E**+

_{0}**P**.)

## Homework Equations

use the laplace equation where the general form of potential is:

[tex]V=\Sigma (A_{l}r^{l}P_{l}(cos(theta))+B_{l}*1/(r_{l+1})*P_{l}(cos(theta)))[/tex]

## The Attempt at a Solution

set the boundary condition when outside of sphere :

r ->infinity, V->0 hence A

_{l}=0

when inside the sphere

r-> 0, V not= infinity hence B

_{l}=0

the next time is to find both the coefficients, a.k.a A

_{l}and B

_{l}. so far am i heading the right directions?

my question is also what

**D**= [tex]\epsilon_{0}[/tex]

**E**+

_{0}**P**purpose here in solving this problem?

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