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

Q. A charged particle of mass m and charge q is released from rest in a uniform electric field E. The kinetic energy of the particle after time t is

(a)(2E² t²)/mq

(b) (Et² m)/(2t² )

(c) (E² q² t²)/2m

(d) (E q m)/2t

Ans: (c)

Sol: Acceleration

$\displaystyle a = \frac{F}{m} = \frac{q E}{m} $

v = u + at

$ \displaystyle v = 0 + \frac{q E}{m}t$

$ \displaystyle K = \frac{1}{2}m v^2 $

$ \displaystyle K = \frac{1}{2}m (\frac{q E t}{m})^2 $

$ \displaystyle K = \frac{q^2 E^2 t^2}{2 m} $