Energy Density

1. Feb 10, 2008

foxjwill

1. The problem statement, all variables and given/known data
I found on Wikipedia the formula for energy density of an electric field in a vacuum to be

$$U = \frac{1}{2}\epsilon_0 E^2.$$

I was wondering if someone could point me in the right direction to figure out how this was derived.

2. Relevant equations

3. The attempt at a solution
I was thinking maybe using Gauss's law?

2. Feb 11, 2008

Shooting Star

It starts with total energy = 1/2[Integral over volume(rho*phi*dV)], where rho is the volume charge density, phi the potential.

Then this has to be written as e0/2[Integral over volume(div E*phi*dV)]. After that you can break up the integrand into two parts.

You can try to do it from here, but it'd best if you look up a book.