# Math Help - Parallel plate capacitor?

1. ## Parallel plate capacitor?

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, $U_i$ and $U_f$
(c) the work required to separate the plates

Spoiler:

$\mbox{(a)}2V$
$\mbox{(b)}\frac{\epsilon_0 AV^2}{2d}$
$\mbox{(c)}\frac{\epsilon_0 AV^2}{2d}\ \frac{\epsilon_0 AV^2}{2d}\ V = L[\sqrt{y^2 + L^2 - y}]\ E_g = \frac{1}{4\pi \epsilon_0}\left[1 - \frac{y}{\sqrt{y^2 + L^2}}\right]$

How to do it?

2. The charge on the capacitor will remain constant.

and Capacitance will vary as $
\frac{\epsilon_0 A}{d}
$

hence capacitance will decrease by a factoor of 2.

$Q=CV$

hence, Potential between the plates will increase by a factor of 2.