Question

The charge on a parallel plate capacitor varies as $q=q_0\cos 2\pi vt$.
The plates are very large and close together (area = A, separation = d).

Neglecting the edge effects, find the displacementcurrent through the capacitor?

Answer 1

Given, charge on parallel plate capacitor,
$q=q_0\cos 2\pi vt$

As we know the current that exists inside the capacitor is Displacement current.

$I_c=I_d=\frac{dq}{dt}$

$I_c=I_d=\frac{d}{dt}$ $\left(q_0\cos 2\pi vt\right)$


$I_c=I_d=-2\pi v{q}_0\sin 2\pi vt$

Final answer: $-2\pi v{q}_0\sin 2\pi vt$