# Simple question about polarized materials

1. Oct 21, 2007

### Devook

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 = $$\frac{k}{r}$$ $$\hat{r}$$

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 = $$Q_{enc}/\epsilon_{0}$$

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 $$Q_{enc}$$ 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?