(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A dielectric sphere of radius R has a uniform permanent polarisationP. Determine the electric field both inside and outside the sphere. (Hint: Since divP= 0 everywhere, the electrostatic potential satisfies Laplace's equation. Do not assume that the sphere is characterised by a dielectric constant. Instead, useD= [tex]\epsilon_{0}[/tex]E+_{0}P.)

2. Relevant 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]

3. 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 whatD= [tex]\epsilon_{0}[/tex]E+_{0}Ppurpose here in solving this problem?

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# Electric Field inside and outside of Dielectric sphere

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