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Question

A parallel plate capacitor with plate area A and initial separation d is connected to battery of EMF V0. work done by external force to increase separation of plates from d to 2d slowly is
[Battery remains connected]

A
ε0AV204d
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B
ε0AV20d
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C
ε0AV202d
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D
ε0AV203d
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Solution

The correct option is A ε0AV204d
Let plate separation be x
Fext=qE=qq2ε0=q22Aε0
dW=Fext dx
W=Fext dx

Given that q=ε0AV0x
W=2ddε0AV202x2dx=ε0AV204d


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