# Homework Help: A point charge inside infinite medium of dielectric

1. Nov 2, 2009

A point charge inside infinite dielectric material

1. The problem statement, all variables and given known data
A point charge is an infinite medium of dielectric material having a relative permittivity $$\epsilonr$$. <--- epsilon(sub r). Find the electric field vector and the potential function at any point in space, assuming that the potential is zero volts at infinity.
2. Relevant equations
D = $$\epsilon$$ * E + P
P = $$\epsilon0$$ * $$\chie$$ vector E
$$\epsilon[\tex] = [tex]\epsilon0$$ * $$\epsilonr$$
$$\chie$$ = $$\epsilonr$$ - 1

well its not letting me put it in right so im gonna enter them in with () next to them
D(vector) = epsilon*E(vector) + P(vector)
P(vector) = epsilon(sub 0)*chi(sub e)*E(vector)
epsilon = epsilon(sub 0)*epsilon(sub r)
chi(sub e) = epsilon(sub r) - 1
Electric Field of Point Charge = k*q/r^2
Electric Field of Sphere = q/(4*pi*epsilon(sub0)*r^2)

3. The attempt at a solution
Im not quiet sure what my first step would be. I would think that a point charge inside a dielectric medium would have a reduced electric field, but it is infinite so wouldnt its electric field be nothing?

Last edited: Nov 2, 2009
2. Nov 2, 2009

### gabbagabbahey

Just use Gauss' Law for $\textbf{D}$....can you think of a Gaussian surface that will exploit the symmetry present?

3. Nov 2, 2009

what do you mean by exploit?

4. Nov 2, 2009

### gabbagabbahey

"Exploit" is just another word for "use"

5. Nov 2, 2009

I feel that a sphere represents a good shape.

6. Nov 2, 2009

### gabbagabbahey

Okay, but why? And where will the center of the sphere be?

7. Nov 2, 2009

The center of the sphere will be located on the point charge

8. Nov 2, 2009

Not quite...What is Gauss' Law in terms of $\textbf{D}$? Do you see why Gauss' Law in terms of $\textbf{E}$ isn't helpful here?