Question

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

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

Answer 1

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

A force is generated because of the elective field

$F=qE\Rightarrow a=\frac{qE}{m}.$

As the particle starts from rest and acceleration is constant applying equation of motion.

$V=u+at$

$V=0+\frac{qEt}{m}$

$V=\frac{qET}{m}$

Then, $KE\frac{1}{2}m{v}^2=\frac{1}{2}m{\left(\frac{qEt}{m}\right)}^2=\frac{1}{2}m\frac{q^2{E}^2{t}^2}{m^2}=\frac{q^2{E}^2{t}^2}{2m}$