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## Homework Statement

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)

## Homework Equations

**[itex]\nabla[/itex]**[itex]\cdot[/itex](ε

_{0}

**E**+

**P**)=ρ

_{f}

and

∫

**D**[itex]\cdot[/itex]d

**a**=q

where the integral is over the closed surface and ρ

_{f}is the charge density of the enclosed free charge.

## The Attempt at a Solution

Using that, I got

**D**=(q/4[itex]\pi[/itex]r

^{2})

**[itex]\hat{r}[/itex]**

And that

**E**

_{r>a}= (1/ε

_{0})

**D**

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