Question

Energy per unit volume for a capacitor having area $A$ and separation $d$ kept at potential difference $V$ is given by:

• A. $\frac{1}{2}{\epsilon }_0\frac{V^2}{d^2}$
• B. $\frac{1}{2{\epsilon }_0}\frac{V^2}{d^2}$
• C. $\frac{1}{2}{C}^{\frac{1}{2}}$
• D. $\frac{{\epsilon }_0^2}{2C}$

Answer 1

The correct option is A $\frac{1}{2}{\epsilon }_0\frac{V^2}{d^2}$

For a parallel plate capacitor: $C=\frac{A{ϵ}_o}{d}$

Volume of capacitor $=Ad$

Energy stored in a capacitor: $E=\frac{1}{2}C{V}^2$

Energy stored per unit volume $E^{\prime }=\frac{\frac{1}{2}C{V}^2}{Ad}$

$\therefore$ $E^{\prime }=\frac{1}{2}\frac{\frac{A{ϵ}_o}{d}{V}^2}{Ad}=\frac{1}{2}{ϵ}_o\frac{V^2}{d^2}$