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Electric Field inside and outside of Dielectric sphere 
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#1
Mar409, 01:54 AM

P: 128

1. The problem statement, all variables and given/known data
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.) 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 what D = [tex]\epsilon_{0}[/tex]E_{0} + P purpose here in solving this problem? 


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