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Question

Physics Question on electrostatic potential and capacitance

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 eneigy stored in the capacitor is

A

12ε0E2\frac{1}{2} \varepsilon_0 E^2

B

E2Adε0\frac{E^2Ad}{\varepsilon_0}

C

12ε0E2Ad\frac{1}{2} \varepsilon_0 E^2 Ad

D

ε0EAd\varepsilon_0 EAd

Answer

12ε0E2Ad\frac{1}{2} \varepsilon_0 E^2 Ad

Explanation

Solution

Capacitance of a parallel plate capacitor is
C=ε0Ad...(i)C = \frac{\varepsilon_0 A}{d}\, \, \, \, ...(i)
Potential difference between the plates is
V=Ed...(ii)V = Ed...(ii)
The energy stored in the capacitor is
U=12CV2=12(ε0Ad)(Ed)2U = \frac{1}{2} CV^2 = \frac{1}{2} \bigg(\frac{\varepsilon_0A}{d} \bigg) (Ed)^2 (Using (i) and (ii))
=12ε0E2Ad\, \, \, = \frac{1}{2} \varepsilon_0 E^2\, Ad