Energy of a charged conductor
When a conductor is charged its potential increases from 0 to V as shown in the graph; and work is done against repulsion, between charge stored in the conductor and charge coming from the source (battery). This work is stored as “electrostatic potential energy”.
In charging capacitor by battery half the energy supplied is stored in the capacitor and remaining half energy (1/2 QV) is lost in the form of heat.
Work done by battery = QV
This stored energy, stored uniformly in the electric field in the volume, Energy density (u) is defined as energy per unit volume (volume = Ad)
We have calculated this for parallel plate, but this is true for all air or vacuum capacitors. If a dielectric medium is completely filled between plates, then energy density becomes