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Homework Help: Conducting sphere surrounded by insulator with dielectric constant

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data

    A conducting sphere of radius A has a charge +Q on it and is surrounded by an insulating material whose dielectric constant varies with radius according to εr = 2exp[-(r/a-1)]2. The dielectric has a spherical outer boundary B. Find the values of D, E, P, ρ as a function of r.

    2. Relevant equations

    εr = 2exp[-(r/a-1)]2,

    Gauss's Law?

    3. The attempt at a solution

    Outside conducting sphere:

    D directed radially outward so using symmetrical surface integral form of Gauss law, D = q/4∏r2.

    E=D/ε0 = q/4∏ε0r2.

    Inside sphere:
    D=0, E=0.

    Not sure if this is right or what next steps to take?
  2. jcsd
  3. Jan 16, 2012 #2


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    Staff Emeritus
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    Hello zhillyz. Welcome to PF!

    I take it that the spherical shell has inner radius A, and outer radius, B.

    E = D/ε0 outside the dielectric shell; where r > B .

    For A < r < B, E = D/εr .
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