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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
A
$\varepsilon_0EAd$
B
$\frac{1}{2}\varepsilon_0E^2$
C
$\frac{E^2Ad}{\varepsilon_0}$
D
$\frac{1}{2}\varepsilon_0E^2Ad$
Detailed Solution
Energy $= \frac{1}{2}CV^2$, with $C = \frac{\varepsilon_0A}{d}$ and $V = Ed$
$= \frac{1}{2}\times\frac{\varepsilon_0A}{d}\times(Ed)^2$
$= \frac{1}{2}\varepsilon_0E^2Ad$
$= \frac{1}{2}\times\frac{\varepsilon_0A}{d}\times(Ed)^2$
$= \frac{1}{2}\varepsilon_0E^2Ad$