A parallel plate capcitor 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_(0)AV^(2))/(d)`
B. `(epsilon_(0)AV^(2))/(2d)`
C. `(epsilon_(0)AV^(2))/(3d)`
D. `(epsilon_(0)AV^(2))/(d)`

Answer

B

Explanation

`C_(1)=(Ain_(0))/(d), U_(1)=(Q^(2))/(2C_(1)),Q=C_(1)V`
`C_(2)=(Ain_(0))/(2d)=(C_(1))/(2), U_(2)=(Q^(2))/(2C_(2))=(Q^(2))/(C_(1))`
`W_(1rarr2)=U_(2)-U_(1)=(Q^(2))/(2C_(1))=((C_(1)V)^(2))/(2C_(1))=(1)/(2)C_(1)V^(2)`
`=(Ain_(0)V^(2))/(2d)`