# Point Charge in a Dielectric Sphere

1. Oct 24, 2012

### KeyToMyFire

1. The problem statement, all variables and given/known data

A point charge q is located at the center of a dielectric sphere of radius a. Find D, E, and P everywhere and plot your results. What is the total bound charge on the surface of the sphere?

(I assume by "everywhere" my professor meant inside and outside the sphere.)
(D is the electric displacement)

2. Relevant equations

$\nabla$$\cdot$(ε0E+P)=ρf

and

D$\cdot$da=q

where the integral is over the closed surface and ρf is the charge density of the enclosed free charge.

3. The attempt at a solution

Using that, I got D=(q/4$\pi$r2)$\hat{r}$

And that Er>a= (1/ε0)D

Beyond that (if that is even correct), I feel like I need more information (or I have no idea what I'm doing).

2. Oct 24, 2012

### TSny

Looks good so far. To go further, maybe you are supposed to assume the material has a certain dielectric constant Ke. So, D = KeεoE. Then you can express your answers for P and E in terms of Ke.