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

Options

A. `x^(-2)`
B. `x`
C. `x^(-1)`
D. `x^(2)`

Answer

A

Explanation

Energy `(U)=(1)/(2)CV^(2)=(1)/(2)((epsi_(0)A)/(x))V^(2)`
`therefore (dU)/(dt)=(1)/(2)epsi_(0)AV^(2)(-(1)/(x^(2))(dx)/(dt))` but `(dx)/(dt)`=velocity (v')
`=-((1)/(2)epsi_(0)AV^(2)V')(1)/(x^(2))`
`therefore (dU)/(dt)prop x^(-2)`