Electric Field inside and outside of Dielectric sphere

  1. 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]E0 + 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 Al=0

    when inside the sphere
    r-> 0, V not= infinity hence Bl=0

    the next time is to find both the coefficients, a.k.a Al and Bl. so far am i heading the right directions?


    my question is also what D = [tex]\epsilon_{0}[/tex]E0 + P purpose here in solving this problem?
     
    Last edited: Mar 4, 2009
  2. jcsd
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