Question

A parallel plate capacitor has a uniform electric field $\overrightarrow{E}$ in the space between the plates. If the distance between the plates is $d$ and the area of each plate is $A$, the energy stored in the capacitor is [${\epsilon }_0-\text{permittivity}$ of free space]

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

Answer 1

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

Energy stored in the capacitor is,

$U=\frac{1}{2}C{V}^2=\frac{1}{2}\times \left(\frac{{\epsilon }_{0}A}{d}\right)\times (Ed{)}^2$

$U=\frac{1}{2}{\epsilon }_{0}A{E}^{2}d[\because V=Ed]$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.