Question

(a) Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.
(b) The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed rectangular loop abcda.

Answer 1

(a)

Energy stored in a capacitor is given by:

$E=\frac{1}{2}C{V}^2$

Using $C=\frac{{\epsilon }_{o}A}{d}$

$E=\frac{1}{2}{\epsilon }_{o}Ad\frac{V^2}{d^2}$

Using potential gradient, $E=\frac{V}{d}$

$\frac{E}{Ad}=\frac{1}{2}{\epsilon }_o{E}^2$

The term on the left hand side is the energy stored per unit volume in a capacitor.

(b)

As electric field is conservative, net work done by electric force in moving a charge through a loop is zero.