Question

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. $\frac{1}{2}\varepsilon_{o}E^{2}$
• B. $\frac{E^{2}Ad}{\varepsilon_{o}}$
• C. $\frac{1}{2}\varepsilon_{o}E^{2}Ad$
• D. $\varepsilon_{o}E^{2}Ad$

Answer 1

Answer: (C)

$\frac{1}{2}\varepsilon_{o}E^{2}Ad$

Answer 2

: Capacitance of a parallel plate capacitor is

$C = \frac{\varepsilon_{0}A}{d}$ …(i)

Potential difference between the plates is

V = Ed …(ii)

The energy stored in the capacitor is

$U = \frac{1}{2}CV^{2} = \frac{1}{2}\left( \frac{\varepsilon_{0}A}{d} \right)(Ed)^{2}$ (using (i) and (ii))

$= \frac{1}{2}\varepsilon_{0}E^{2}Ad$