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

Answer 1

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

The energy stored in the capacitor is, $U=\frac{1}{2}C{V}^2...\left(1\right)$
Capacitacne of a parallel plate capacitor is, $C=\frac{{\epsilon }_{0}A}{d}....\left(2\right)$
Potential difference between the plates is $V=E\times d...\left(3\right)$

On putting the values from eq. $2$ and $3$ to eq. $1$,
$=\frac{1}{2}\times {\epsilon }_0\frac{A}{d}\times (E\times d{)}^2$
$=\frac{1}{2}{\epsilon }_0{E}^{2}Ad$
Hence, option D is correct.