If the distance between two parallel plates of a capacitor is $d$, $A$ is the area of each plate, and $E$ is the electric field, find the energy stored in the capacitor.

(Shift I - Memory Based)

Question

If the distance between two parallel plates of a capacitor is $d$, $A$ is the area of each plate, and $E$ is the electric field, find the energy stored in the capacitor. (Shift I - Memory Based)

YESPYQ · Accepted Answer

Correct answer: a) $\frac{1}{2}{E}^{2}A{ϵ}_{0}d$. The capacitance of the parallel plate capacitor is: $C={ϵ}_{0}\frac{A}{d}\mathrm{.}$ Energy stored in a capacitor: $U=\frac{1}{2}C{V}^{2}\mathrm{.}$ Substituting $V=Ed$ and $C={ϵ}_{0}\frac{A}{d}$​: $U=\frac{1}{2}{ϵ}_{0}\frac{A}{d}(Ed{)}^{2}=\frac{1}{2}{E}^{2}A{ϵ}_{0}d\mathrm{.}$ Thus, the energy stored is $\frac{1}{2}{E}^{2}A{ϵ}_{0}d$

If the distance between two parallel plates of a capacitor is \(d\), \(A\) is the area of each plate, and \(E\) is the e…

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