A parallel plate condenser has a uniform electric field $E(\mathrm{~V} / \mathrm{m})$ in the space between…
A parallel plate condenser has a uniform electric field $E(\mathrm{~V} / \mathrm{m})$ in the space between the plates. If the distance between the plates is $d(\mathrm{~m})$ and area of each plate is $A\left(\mathrm{~m}^2\right)$ the energy (joule) stored in the condenser is
$\frac{1}{2} \varepsilon_0 E^2$
$\varepsilon_0 E A d$
$\frac{1}{2} \varepsilon_0 E^2 A d$
$E^2 A d / \varepsilon_0$
Solution
The energy stored in the condenser
$\begin{aligned}
& U=\frac{1}{2} C V^2 \\
& U=\frac{1}{2}\left(\frac{A \varepsilon_0}{d}\right)(E d)^2 \quad\left(\because C=\frac{A \varepsilon_0}{d} \text { and } V=E d\right) \\
& U=\frac{1}{2} \varepsilon_0 E^2 A d
\end{aligned}$