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Electrostatic Potential and Capacitance

Capacitor and capacitance

A capacitor is given a charge q. The distance between the plat

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Medium

Solving time: 3 mins

A capacitor is given a charge q. The distance between the plates of the capacitor is $d$ . One of the plates is fixed and the other plate is moved away from the other till the distance between them becomes $2 d$ . Find the work done by the external force.

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Book:

Electricity and Magnetism (DC Pandey)

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Henry Discussed

A capacitor is given a charge q. The distance between the plates of the capacitor is

d

. One of the plates is fixed and the other plate is moved away from the other till the distance between them becomes

2 d

. Find the work done by the external force.

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Solution When one plate is fixed, the other is attracted towards the first with a force

F = \frac{q ^{2}}{2 A ε _{0}} = constant

Hence, an external force of same magnitude will have to be applied in opposite direction to increase the separation between the plates.

∴

W = F (2 d - d) = \frac{q ^{2} d}{2 A ε _{0}}

Alternate solution

W = Δ U = U_{f} - U_{i} = \frac{q ^{2}}{2 C _{f}} - \frac{q ^{2}}{2 C _{i}}

Here,

C_{f} = \frac{ε _{0} A}{2 d} and C_{i} = \frac{ε _{0} A}{d}

Substituting in Eq. (i), we have

W = \frac{q ^{2}}{2 ( \frac{ε _{0} A}{2 d} )} - \frac{q ^{2}}{2 ( \frac{ε _{0} A}{d} )} = \frac{q ^{2} d}{2 ε _{0} A}

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Question Text	A capacitor is given a charge q. The distance between the plates of the capacitor is $d$ . One of the plates is fixed and the other plate is moved away from the other till the distance between them becomes $2 d$ . Find the work done by the external force.
Topic	Electrostatic Potential and Capacitance
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	117

A capacitor is given a charge q. The distance between the plates of the capacitor is $d$ . One of the plates is fixed and the other plate is moved away from the other till the distance between them becomes $2 d$ . Find the work done by the external force.

Text solutionVerified

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