. E NERGY S TORED IN A C APACITOR A capacitor, as we have seen above, is a system of two conductors with charge Q and – Q . To determine the energy stored in this configuration, consider initially two uncharged conductors and . Imagine next a process of transferring charge from conductor to conductor bit by bit, so that at the end, conductor gets charge Q .
By charge conservation, conductor has charge – Q at the end (Fig . ) . In transferring positive charge from conductor to conductor , work will be done externally, since at any stage conductor is at a higher potential than conductor . To calculate the total work done, we first calculate the work done in a small step involving transfer of an infinitesimal (i.e., vanishingly small) amount of charge.
Consider the intermediate situation when the conductors and have charges Q ′ and – Q ′ respectively. At this stage, the potential difference V ′ between conductors to is Q ′ / C , where C is the capacitance of the system. Next imagine that a small charge δ Q ′ is transferred from conductor to . Work done in this step ( δ W ′ ), resulting in charge Q ′ on conductor increasing to Q ′ + δ Q ′ , is given by Q W Q Q δ δ δ ′ ′ ′ ′ ( .
) FIGURE . (a) Work done in a small step of building charge on conductor from Q ′ to Q ′ + δ Q ′ . (b) Total work done in charging the capacitor may be viewed as stored in the energy of electric field between the plates.