Question

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

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

Answer 1

The correct option is A $\frac{1}{2}{\epsilon }_0{E}^{2}Ad$

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

Capacitance of parallel plate capacitor $=\frac{{ϵ}_{0}A}{d}$

Potential difference across parallel plate capacitor due to presence of electric field, $V=E\times d$

Thus, energy stored in capacitor $=\frac{1}{2}\left(\frac{{ϵ}_{0}A}{d}\right)(Ed{)}^2$$=\frac{1}{2}{ϵ}_0{E}^{2}Ad$