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Simple question about polarized materials

  1. Oct 21, 2007 #1
    1. The problem statement, all variables and given/known data
    A thick spherical shell of inner radius a and outer radius b is made of dielectric material with a "frozen-in" polarization

    P = [tex]\frac{k}{r}[/tex] [tex]\hat{r}[/tex]

    where k is a constant and r is the distance from the center. Find the electric field in all three regions.

    2. Relevant equations
    Gauss's Law: E*A = [tex]Q_{enc}/\epsilon_{0}[/tex]


    3. The attempt at a solution
    Basically my question is simple. I've done the whole thing; I have a solution. The problem is that I don't believe the solution. Shouldn't the [tex]Q_{enc}[/tex] for the region where r > b be 0? Since there are no free charges, isn't the material made completely of dipoles because it is a dielectric, and if that is the case shouldn't each positive pole cancel each negative pole causing the enclosed charge to be zero?
     
  2. jcsd
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