Question

A parallel plate capacitor whose capacitance $C$ is $14\text{pF}$ is charged by a battery to a potential difference $V=12\text{V}$ between its plates. The charging battery is now disconnected and a porcelain plate with $k=7$ is inserted between the plates, then the porcelain plate would oscillate back and forth between the plates of capacitor, with a constant mechanical energy of _______ $\text{pJ}$.
$($Assume no friction$)$

Answer 1

Initial energy stored in capacitor is,
$U_i=\frac{1}{2}C{V}^2$

$=\frac{1}{2}\times 14\times (12{)}^2\text{pJ}$

$=1008\text{pJ}$

Final energy stored in capacitor is,
$U_f=\frac{Q^2}{2kC}$

$=\frac{(14\times 12{)}^2}{2\times 7\times 14}$

$=144\text{pJ}$

Oscillating energy $=U_i-U_f$
$=1008-144$
$=864\text{pJ}$