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What is the total charge on the surface?

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data
    A point charge q is embedded at the centre of a sphere of linear dielectric material (with susceptibility chi(subscript e) and radius R).

    b)What is the total charge on the surface? [3 marks]
    c) where is the compensating negative bound charge located? calculate it


    3. The attempt at a solution

    volume polarisation charge density=-div P
    =1/r^2 d/dr((r^2)P) (partial derivative)
    =1/r^2 d/dr [[(r^2 Q chi(e) epsilon0]/[4 pi epsilon(r) r^2]]
    =1/R^2 d/dr [(q chi(e) epsilon0)/(4 pi epsilon (r))]
    =1/R^2 *0
    =0


    surface charge polarisation density=[(q chi(e) epsilon0) r-hat.n]/(4 pi epsilon1 R^2)
    =[(q chi(e) epsilon0)]/(4 pi epsilon1 R^2)

    does that help to calculate the total bound charge on the surface at all?
    because the surface polarisation charge density=0, the bound charge on the surface=0. three marks for saying just that?

    please tell me if I'm wrong
     
    Last edited: Oct 30, 2011
  2. jcsd
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