To determine the energy stored in
capacitor, consider initially two uncharged conductors 1 and 2. Imagine next a
process of transferring charge from conductor 2 to conductor 1 bit by bit, so
that at the end, conductor 1 gets charge

*Q*.
By charge conservation, conductor 2 has
charge –

*Q*at the end.
In transferring positive charge from
conductor 2 to conductor 1, work will be done externally, since at any stage
conductor 1 is at a higher potential than conductor 2.

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 1 and 2 have charges

*Q'*^{ }and –*Q'*respectively. At this stage, the potential difference*V*^{'}between conductors 1 to 2 are*Q'*/*C*, where*C*is the capacitance of the system.
Next imagine that a small charge δ

*Q'*^{ }is transferred from conductor 2 to 1. Work done in this step (δ*W'*), resulting in charge*Q'*on conductor 1 increasing to*Q'*+ δ*Q'*, is given by
The total work done (

*W*) is the sum of the small work (δ*W*) over the very large number of steps involved in building the charge*Q*^{'}from zero to*Q*.
The same result can be obtained directly
from Eq. by integration

The surface charge density s is related to the electric field

*E*between the plates,
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