Deriving Electric Field Energy Density

[foxjwill]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

I was thinking maybe using Gauss's law?

 

[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.