# Electric Field Energy Density

1. Oct 7, 2007

### mystify

1. The problem statement, all variables and given/known data
Provide a proof for the electric field energy density of an arbitrary charge distribution using basic notions of electrostatics.

2. Relevant equations
The energy density for an electric field is $w = \frac{1}{2} \epsilon E^2$

3. The attempt at a solution
I am not sure at all what kind of energy formula to derive. I computed the elementary work done by the field on an external electrical charge, then divided it by the elementary unit of volume in spherical coordinates, but to no avail.

How to proceed ?

2. Oct 9, 2007

### Gokul43201

Staff Emeritus
I guess you are to derive an expression for the energy density at a point $\vec{R}$ due to a charge distribution given by $\rho (\vec{r})$.