Question

A charged particle of mass $m$ and charge $q$ is released from rest in a uniform electric field $E$. Neglecting the effect of gravity, the kinetic energy of charged particle after $t$ seconds is

• A. $\frac{E{q}^{2}m}{2t^2}$
• B. $\frac{E^2{q}^2{t}^2}{2m}$
• C. $\frac{2E^2{t}^2}{qm}$
• D. $\frac{Eqm}{t}$

Answer 1

The correct option is B $\frac{E^2{q}^2{t}^2}{2m}$

Force on particle=$F=qE$

Hence, acceleration of particel$=a=\frac{F}{m}=\frac{qE}{m}$

Initial speed$=u=0$

Hence, final velocity$=v=u+at=\frac{qEt}{m}$

Kinetic energy=$K=\frac{1}{2}m{v}^2=\frac{1}{2}m{\left(\frac{qEt}{m}\right)}^2$

$⟹K=\frac{E^2{q}^2{t}^2}{2m}$

Answer-(B)