SATHEE: Electrostatic Potential and Capacitance

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) $\frac{1}{2} ε_{0} E^{2}$

(b) $E^{2} A d / ε_{0}$

(d) $ε_{0} E A d$

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Answer:

Correct Answer: 32. (c)

Solution:

$U = \frac{1}{2} C V^{2}$

$V$ is the p.d. between two plates of the capacitor potential difference $V = E . d$ .

The capacitance of the parallel plate capacitor

$C = \frac{A ε_{0}}{d}$

Substituting the value of $C$ in equation (i)

$U = \frac{1}{2} \frac{A ε_{0}}{d} (E d)^{2} = \frac{1}{2} A ε_{0} E^{2} d$

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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 :

Answer:

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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 :