Average electric field in spherical volume

1. Apr 21, 2010

jam357

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

Show that the average electric field within a spherical region, due to a single point charge, q at a distance r from the center, within the sphere is the same as the field at r due to a uniformly charged sphere with charge density p = -3q/4pi(R^3)

2. Relevant equations

3. The attempt at a solution

I can set up the integral for the average electric field, but run into problems when trying to evaluate it. I don't know whether there is a better way to tackle this problem, but i would appreciate any advice on how to tackle this problem.
This is a problem out of Griffiths Intro to Electrodynamics, problem 3.41
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 21, 2010

gabbagabbahey

Direct integration is the only way, so show us the integral you've come up with.

3. Apr 23, 2010

jam357

The integral is not particularly nice, but i found a more cunning way to solve the problem, but thanks anyway. I also don't know how to write mathematical expressions on this thing