A parallel plate capacitor has plate area `A` and separation `d`. It is charged to a potential difference `V_(0)`. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is

Options

A. `(3epsilon_0AV_0^2)/(d)`
B. `(epsilon_0AV_0^2)/(d)`
C. `(epsilon_0AV_0^2)/(3d)`
D. `(epsilon_0AV_0^2)/(d)`

Answer

D

Explanation

`U_i=1/2CV^2=1/2(Aepsilon_0)/dV_0^2and Q=CV=(Aepsilon_0V_0)/d`
`U_f=Q^2/(2C)=(A^2epsilon_0^2V_0^2)/(2d^2(Aepsilon_0)/(3d))=(3Aepsilon_0V_0^(2))/(2d)`
`W=U_f-U_i(Aepsilon_0V_0^2)/d`