A charged particle of mass `m` and charge `q` is released from rest in an electric field of constant magnitude `E`. The kinetic energy of the particle after time `t` is

Options

A. `(Eq^(2)m)/(2t^(2))`
B. `(2E^(2)t^(2))/(mq)`
C. `(E^(2)q^(2)t^(2))/(2m)`
D. `(Eqm)/t`

Answer

C

Explanation

When charge q is released in uniform electric field E then its acceleration
`q=(qE)/m`
So, its motion will be uniformly accelerated motion and its velocity after t second is given by
`v=at=(qE)/m t`
The KE of charged particle
`KE=1/2 mv^(2)=1/2 mv^(2)= 1/2 m ((qE)/2 t )^(2)=(q^(2)E^(2)t^(2))/(2m)`