Question

A charge $+q$ having mass $m$ is released from rest in a uniform electric field $E$ momentum acquired by the charge after time $t$ is:

• A. $\frac{q^2{E}^2{t}^2}{2m}$
• B. $\frac{qEt}{m}$
• C. $qEt$
• D. None of these.

Answer 1

Answer: (A)

$\frac{q^2{E}^2{t}^2}{2m}$

initial velocity $u=0,$

acceleration $a=qE/m,$

time $t=t,$

final velocity $v=?$

by $v=u+at,$ we get

$v=0+\left(\frac{qE}{m}\right)t$

$orv=\frac{qEt}{m}$

so the final kinetic energy is

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

$\Rightarrow K\left(t\right)=\frac{q^2{E}^2{t}^2}{2m}$

Hence,

option $\left(A\right)$ is correct answer.