Question

A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A$, the energy stored in the capacitor is :

• A. $E^{2}Ad/{\epsilon }_0$
• B. $\frac{1}{2}{\epsilon }_0{E}^{2}Ad$
• C. ${\epsilon }_{0}EAd$
• D. $\frac{1}{2}{\epsilon }_0{E}^2$

Answer 1

Answer: (B)

For a capacitor,
Total energy = $\frac{1}{2}C{V}^2$ = energy density$\times$ volume, where C = $\frac{{ϵ}_{0}A}{d}$, $V=Ed$
$U=\left(\frac{1}{2}{\in }_0{E}^2\right)\left(Ad\right)$