The energy required to charge a parallel plate condenser of plate separtion `d` and plate area of cross-section `A` such that the unifom field between the plates is `E` is

Options

A. `epsilon_(0)E^(2)Ad`
B. `(1)/(2)epsilon_(0)E^(2)Ad`
C. `(1)/(2)epsilon_(0)E^(2)//Ad`
D. `epsilon_(0)E^(2)//Ad`

Answer

A

Explanation

Energy stored in capacitor for field
`E=(1)/(2)CV^(2)`
`=(1)/(2)((epsilon_(0)A)/(d))(E.d)^(2)`
`=(1)/(2)epsilon_(0)AE^(2)d`
Energy stored in capacitor `+` Energy loss in the process of charging = Energy given by cell.
`=(Aepsilon_(0))/(d)V^(2)`
`=2xx" Energy stored in capacitor"`
Since energy stored in capacitor = Energy loss in the process of storing the charge in capacitor.