Point Charge in a Dielectric Sphere

[KeyToMyFire]

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

$\nabla$$\cdot$(ε₀E+P)=ρ_f

and

∫D$\cdot$da=qwhere 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$\pi$r²)$\hat{r}$

And that E_r>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).

 

[TSny]

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