A parallel plate capacitor has a uniform electric field in the space between the plates. If the distance between the plates is and the area of each plate , the energy stored in the capacitor is ( = permittivity of free space) [2021]

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Q.
A parallel plate capacitor has a uniform electric field $' \vec{E}'$ in the space between the plates. If the distance between the plates is $' d'$ and the area of each plate $' A'$ , the energy stored in the capacitor is ( $ε_{0}$ = permittivity of free space) [2021]

1 $\frac{E^{2} A d}{ε_{0}}$

2 $\frac{1}{2} ε_{0} E^{2}$

3 $ε_{0} E A d$

4 $\frac{1}{2} ε_{0} E^{2} A d$

Ans.
(4)

The capacitance of a parallel plate capacitor of plate area $A$ and separation $d$ is given by

$C = \frac{ε_{0} A}{d}$

The potential is given by $V = E d$

Where $E$ is electric field.

Energy, $U = \frac{1}{2} C V^{2} = \frac{1}{2} \times \frac{ε_{0} A}{d} \times E^{2} d^{2}; U = \frac{1}{2} ε_{0} E^{2} A d$

Solution

Q.
A parallel plate capacitor has a uniform electric field $' \vec{E}'$ in the space between the plates. If the distance between the plates is $' d'$ and the area of each plate $' A'$ , the energy stored in the capacitor is ( $ε_{0}$ = permittivity of free space) [2021]

1 $\frac{E^{2} A d}{ε_{0}}$

2 $\frac{1}{2} ε_{0} E^{2}$

3 $ε_{0} E A d$

4 $\frac{1}{2} ε_{0} E^{2} A d$

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Solution

Q. 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 the area of each plate 'A', the energy stored in the capacitor is (ε0 = permittivity of free space) [2021]

1 E2Adε0

2 12ε0E2

3 ε0EAd

4 12ε0E2Ad

Ans. (4) The capacitance of a parallel plate capacitor of plate area A and separation d is given by C=ε0Ad The potential is given by V=Ed Where E is electric field. Energy, U=12CV2=12×ε0Ad×E2d2 ; U=12ε0E2Ad

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Q.
A parallel plate capacitor has a uniform electric field $' \vec{E}'$ in the space between the plates. If the distance between the plates is $' d'$ and the area of each plate $' A'$ , the energy stored in the capacitor is ( $ε_{0}$ = permittivity of free space) [2021]

1 $\frac{E^{2} A d}{ε_{0}}$

2 $\frac{1}{2} ε_{0} E^{2}$

3 $ε_{0} E A d$

4 $\frac{1}{2} ε_{0} E^{2} A d$