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Question

The plate separation in a parallel plate condenser is d and plate area is A. If it is charged to V volt and battery is disconnected then the work done in increasing the plate separation to 2d will be


A

32ϵ0AV2d

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B

ϵ0AV2d

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C

2ϵ0AV2d

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D

ϵ0AV22d

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Solution

The correct option is A

32ϵ0AV2d


q=CV=(ε0Ad)V

After charging q will become constant.

W=UfUi

=q22Cfq22Ci

=q22(1Cf1Ci)

=(ε0AV/d2)2(2dε0Adε0A)

=ε0AV22d


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