Electrostatic Potential and Capacitance - Result Question 30
32. 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 :
[2012M, 2011, 2008]
(a) $\frac{1}{2} \varepsilon_0 E^{2}$
(b) $E^{2} A d / \varepsilon_0$
(c) $\frac{1}{2} \varepsilon_0 E^{2} A d$
(d) $\varepsilon_0 E A d$
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Answer:
Correct Answer: 32. (c)
Solution:
- (c) The energy stored by a capacitor
$U=\frac{1}{2} C V^{2}$
$V$ is the p.d. between two plates of the capacitor potential difference $V=E . d$.
The capacitance of the parallel plate capacitor
$C=\frac{A \varepsilon_0}{d}$
Substituting the value of $C$ in equation (i)
$U=\frac{1}{2} \frac{A \varepsilon_0}{d}(E d)^{2}=\frac{1}{2} A \varepsilon_0 E^{2} d$
