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

Options

A. `(1)/(2) epsilon_(0)E^(2)`
B. `(E^(2)Ad)/(epsilon_(0))`
C. `(1)/(2) epsilon_(0)E^(2) Ad`
D. `epsilon_(0)Ead`

Answer

C

Explanation

Capacitance of a parallel plate capacitor is
`C = (epsilon_(0)A)/(d)` …(i)
Potential difference between the plates is
V = Ed …(ii)
The energy stored in the capacitor is
`U = (1)/(2)CV^(2) = (1)/(2)((epsilon_(0)A)/(d)) (Ed)^(2)` (Using (i) and (ii))
`= (1)/(2) epsilon_(0) E^(2) Ad`