Problem

A parallel-plate capacitor has plates of area

A

and separation

d

and is charged to a potential difference

V

. The charging battery is then disconnected, and the plates are pulled apart until their separation is

2d

. Derive expression in terms of

A

d

and

V

for (a) the new potential difference (b) the initial and final stored energies,

U_i

and

U_f

and (c) the work required to increase the separation of plates from

d

2d