Energy Density in an Electric Field

Equation (i) can be written in a form that shows that the energy stored in a capacitor is proportional to the square of the strength of the electric field. Substituting V_f = E × d and C = ε₀A d into Equation (i) 

.........(i)

gives

where we note that A × d is the volume inside the capacitor.

Since the energy stored in the capacitor is proportional to the volume occupied by the electric field, we see that the energy per unit volume, the energy density, is simply given by

This result, that the energy density in an electric field is proportional to the square of the strength of the field, turns out to be a far more general result than we might expect from the above derivation. It applies not just to the uniform electric field in an idealized capacitor, but to electric fields of arbitrary shape.