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Q.

A parallel plate capacitor of plate area A and plate separation d charged by a battery of voltage V. The battery is then disconnected. The work needed to pull the plates to separation 2d is 

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a

2AV2ε0d

b

3AV2ε0d

c

AV2ε0d

d

AV2ε02d

answer is C.

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Detailed Solution

Energy stored initially is Ui=Q22C. if d is doubled, C becomes C / 2.Hence, energy stored when d is doubled is Uf=Q2C
 Work needed is
W=Uf-Ui=Q22C2-Q22C=Q22C=12CV2
(Q=CV)
NowC=Aε0d. Hence
W=Aε0V22d.

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