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  4. Energy stored in between the plates of parallel plate capacitor of area A, separated by distance d is

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Q. Energy stored in between the plates of parallel plate capacitor of area A, separated by distance d is

AIIMSAIIMS 2011Electrostatic Potential and Capacitance

Solution:

Energy stored in capacitor of capacitance C with voltage V is, $U=\frac{1}{2}CV^{2}$
but $C=\frac{\varepsilon_{0}A}{d}, V=Ed$
where A is the area of capacitor plate and d is the distance of separation and E is the electric field.
$\therefore U=\frac{1}{2} \frac{\varepsilon_{0}A}{d}E^{2}d^{2}$
$=\frac{1}{2}\varepsilon_{0} E^{2} \,Ad$