A parallel plate capacitor has a uniform electric field $\vec{E}$ in the space between the plates. If the dist

Question

A parallel plate capacitor has a uniform electric field $\vec{E}$ 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 ($\varepsilon_0$ = permittivity of free space)

Accepted Answer

Energy density associated with electric field is given by $u = \frac{dU}{dV} = \frac{1}{2} \varepsilon_0 E^2$. Total energy stored $U = \int dU = \int \frac{1}{2} \varepsilon_0 E^2 dV = \frac{1}{2} \varepsilon_0 E^2 \int dV = \frac{1}{2} \varepsilon_0 E^2 V = \frac{1}{2} \varepsilon_0 E^2 Ad$.

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