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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: ($\epsilon_0$ = permittivity of free space)
A
$\epsilon_0EAd$
B
$\frac{1}{2}\epsilon_0E^2Ad$
C
$\frac{E^2Ad}{\epsilon_0}$
D
$\frac{1}{2}\epsilon_0E^2$
Detailed Solution
$U = \frac{1}{2}CV^2$ with $C = \frac{\epsilon_0A}{d}$ and $V = Ed$
$U = \frac{1}{2}\left(\frac{\epsilon_0A}{d}\right)(Ed)^2 = \frac{1}{2}\epsilon_0E^2Ad$