Question

A parallel plate condenser has a uniform electric field E (V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is $A\left(m^2\right)$ the energy (joules) stored in the condenser is :

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

Answer 1

The correct option is D $\frac{1}{2}{ϵ}_0{E}^{2}Ad$

The capacitance of parallel plate condenser is $C=\frac{A{ϵ}_0}{d}$ and potential difference between the plates is $V=Ed$.
Energy stored, $U=\frac{1}{2}C{V}^2=\frac{1}{2}\left(\frac{A{ϵ}_0}{d}\right)(Ed{)}^2=\frac{1}{2}A{ϵ}_0{E}^{2}d$