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A parallel plate capacitor is connected ...

A parallel plate capacitor is connected to a battery. The plates are pulled apart with uniform speed. If x is the separation between the plates, then the rate of change of electrostatic energy of the capacitor is proportional to

A

`x^2`

B

`x`

C

`1/x`

D

`1/x^2`

Text Solution

Verified by Experts

The correct Answer is:
D
d. The capacitance of capacitor `C` is `(epsilon_(0)AV)/(x):U=(1)/(2)qV=(1)/(2)(epsilon_(0)AV^(2))/(2 x)`
So, `(du)/(dt)=(1)/(2)epsilon_(0)AV^(2) (-(1)/(x^(2)))(dx)/(dt)`
`=(1)/(2)epsilon_(0)AV^(2)V(-(1)/(x^(2)))`
From the earlier expression,
`(dU)/(dt)prop(1)/(x^(2))`
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