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Conducting Sphere Covered By Spherical Dielectric

  1. Oct 26, 2009 #1

    An isolated metal sphere of radius a has a free charge Q on its surface. The sphere is covered with a dielectric layer with inner radius a and outer radius b

    Calculate the polarization charge density on the inside and outside of the dielectric.

    2. Relevant equations

    3. The attempt at a solution
    So I know that the electric field outside of the conducting sphere w/o dielectric is:

    [tex]E = \frac{k Q}{r^2}[/tex]

    This field however, should have the electric field due to the dielectric subtracted from it.

    If we can regard the dielectric as a capacitor since it has an equal amount of polarized charge on its inner and outer surfaces, the electric field for a < r < b should be:

    [tex]E = \frac{k q'}{r^2}[/tex] where q'=charge on inner surface of dielectric

    the charge on the inner surface should just be

    [tex]q' = \sigma_{inner} 4 \pi a^2[/tex]

    now I know I want [tex]\sigma_{inner}[/tex], and then it would be simple to find [tex]\sigma_{outer}[/tex], but im not really sure how to solve for it
  2. jcsd
  3. Oct 26, 2009 #2
    or is this totally wrong?

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