Energy of a parallel plate capacitor homework

[Tonythaile]

Hi all

"A parallel plate capacitor in which plates of area A are separated by a distance d, has a capacitance C = $\frac{Aε_{0}ε_{r}}{d}$
It is charged to a pd V. Neglecting edge effects, derive an equation for the electric field E in the capacitor, and show that the energy stored per unit volume is w= 0.5$ε_{r}ε_{0}E^{2}$"

I believe that the electric field in a capacitor to be equal to $\frac{\sigma}{\epsilon_{0}}$
via Gauss Law, and using V = Ed you can then get V = $\frac{\sigma d}{\epsilon_{0}}$.

I have then tried to use the various equations for work done = 0.5CV^2, 0.5QV etc to no avail.

Any help much appreciated.

Thanks

 

[rude man]

Hi all

"A parallel plate capacitor in which plates of area A are separated by a distance d, has a capacitance C = $\frac{Aε_{0}ε_{r}}{d}$
It is charged to a pd V. Neglecting edge effects, derive an equation for the electric field E in the capacitor, and show that the energy stored per unit volume is w= 0.5$ε_{r}ε_{0}E^{2}$"

I believe that the electric field in a capacitor to be equal to $\frac{\sigma}{\epsilon_{0}}$
Thanks

That would be correct if the interplate material is air, but it's not.