Point Charge in a Dielectric Sphere

  • #1

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](ε0E+P)=ρf

and

D[itex]\cdot[/itex]da=q


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

The Attempt at a Solution



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

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).
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,798
3,156
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.
 

Related Threads on Point Charge in a Dielectric Sphere

Replies
1
Views
6K
Replies
6
Views
7K
Replies
1
Views
5K
  • Last Post
Replies
0
Views
2K
Replies
8
Views
3K
Replies
1
Views
1K
Replies
8
Views
8K
Replies
1
Views
1K
Replies
5
Views
4K
Top