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A parallel plate air capacitor has initi...

A parallel plate air capacitor has initial capacitance C. If plate separation is slowly increased from `d_(1)` to `d_(2)`, then mark the correct statement (s). (Take potential of the capacitor to be constant, i.e. throughout the process it remains connected to battery.)

A

Work done by electric force=negative of work done by external agent.

B

Work done by external force`=-intoverset(vec)F.overset(vec)dx,` where `overset(vec)(F)` is the electric force of attraction between the plates at plate setaration `x`.

C

Work done by electric force `ne`negative of work done by external agent.

D

Work done by battery `=` two times the change in electric potential energy stored in capacitor.

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`C=(epsilon_(0)A)/d_(1), C'=(epsilon_(0)A)/d_(2)`
Extra charge flown `=Q'=Q(C'-C)V`
`=epsilon_(0)AV[1/d_(2)-1/d_(1)]`
Work done by battery is
`W_(b)=Vxx"charge flown"=epsilon_(0)AV^(2)[1/d_(2)-1/d_(1)]`
Change in potential energy of capacitor is
`DeltaU=1/2(C'-C)V^(2)`
`=1/2epsilon_(0)AV^(2)[1/d_(2)-1/d_(1)]`.
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