A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance…
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
$\frac{1}{2} \varepsilon_0 E^2$
$E^2 A d / \varepsilon_0$
$\frac{1}{2} \varepsilon_0 E^2 A d$
$\varepsilon_0 E A d$
Solution
Energy density for a parallel plate capacitor $=\frac{1}{2} \varepsilon_0 E^2$ and volume $=A d$
Total energy $=$ energy density $\times$ volume
$\begin{aligned}
& =\left(\frac{1}{2} \varepsilon_0 E^2\right) \times(A d) \\
& =\frac{1}{2} \varepsilon_0 E^2 A d
\end{aligned}$
.