1.11 Energy Storage in a Capacitor
The work required to move a unit of charge q across the plates of a capacitor is equal to qV, where V is the voltage across the plates of the capacitor. When the capacitor is discharged there is no voltage and the work required to move the first unit of charge is zero. When the second unit of charge is moved it must do work against the field created by the first unit of charge. The work required to move the last unit of charge is qV. On average, the work done in moving a total charge Q is 1/2QV.
The energy stored in a capacitor can be expressed in terms of the capacitance by noting that the ratio of Q/V is the capacitance C. Using this relationship, the energy in a capacitor is given by