An air filled parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If…
An air filled 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 ' $A^{\prime}$, the energy stored in the capacitor is $\left(\epsilon_{0}=\right.$ permittivity of free space)
$\frac{1}{2} \in_{0} \mathrm{E}^{2} \mathrm{Ad}$
$\mathrm{E}^{2} \frac{\mathrm{Ad}}{\epsilon_{0}}$
$\frac{1}{2} \in_{0} \mathrm{E}^{2}$
$\mathrm{E}_{0} \mathrm{E} \mathrm{Ad}$
Solution
Energy per unit volume in an electric field is
$U=\frac{1}{2} \epsilon_{\mathrm{o}} E^{2}$
Volume of the space between the plates is $=\mathrm{Ad}$
$\therefore$ Energy stored in the electric field $=\frac{1}{2} \epsilon_{0} E^{2} \mathrm{Ad}$