Energy stored in a capacitor:  A capacitor is a device to store energy. The process of charging up a capacitor involves the transferring of electric from its one plate to another. The work done in charging the capacitor is stored as its electrical potential energy.

Expression for the energy stored in a capacitor: Consider a capacitor or capacitance C. initially its two plates is uncharged. Suppose the positive charge is transferred from plate 2 to plate 1 but by bit. In this process, external work has to be done because at any stage plate 1 is at higher potential than plate 2. Suppose fig. then the potential difference between the two plates will be

V = Q/C

Suppose now a small additional charge dQ be transferred from plate 2 plate 1.

The work done will be dW = VdQ = (Q/C) dQ

The total work done in transferring a charge Q from plate 2 plate 1 will be

W =

This work done is stored as electrical potential energy U of the capacitor.

Energy density of an electric field:

Consider a parallel plate capacitor having plate area A and plate separation d then capacitance is given by

As

 σ = ɛ₀E

Charge on either plate of the capacitor is

Q = σA = ɛ₀EA

 

Where Ad is the volume

Then energy of the electric field is given by