A parallel plate condenser has a unifrom electric field `E (V//m)` in the space between the plates. If the distance between the plates is `d(m)` and area of each plate is `A(m^(2))` the energy (joule) stored in the condenser is

Options

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

Answer

D

Explanation

Capacitance of a parallel plate condenser with dielectric is
`C=(k epsilon_(0)A)/d`………i
Potential difference across the plates is
`V=E//kd`………….ii
Energy stored in the condenser is
`U=1/2CV^(2)`
`=1/2((k epsilon_(0)A)/d)(E//kd)^(2)`
[ Using Eqs (i) and (ii)]
`=1/(2k)epsilon_(0)E^(2)Ad`