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 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, $\displaystyle U_i$ and $\displaystyle U_f$

(c) the work required to separate the plates

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