Question

A particle of mass $M$ and charge $q$ is released from rest in a region of uniform electric field of magnitude $E$. After a time $t$, the distance traveled by the charge is $S$ and the kinetic energy attained by the particle is $T$. Then, the ratio $T/S$ :

• A. remains constant with time $t$
• B. varies linearly with the mass $M$ of the particle
• C. is independent of the charge $q$
• D. is independent of the magnitude of the electric field $E$

Answer 1

The correct option is A remains constant with time $t$

Acceleration of the particle $a=\frac{F_e}{M}=\frac{qE}{M}$

Initial velocity of the particle is zero i.e. $u=0$

Its velocity after time $t$, $v=u+at$

$⟹$ $v=0+at=at$

Distance it covered in time $t$, $S=ut+\frac{1}{2}a{t}^2$

$⟹$ $S=0+\frac{1}{2}a{t}^2=\frac{a{t}^2}{2}$

Kinetic energy attained $T=\frac{1}{2}M{v}^2=\frac{1}{2}M{a}^2{t}^2$

Thus the ratio $\frac{T}{S}=\frac{M{a}^2{t}^2/2}{a{t}^2/2}=Ma$

$⟹$ $\frac{T}{S}=M\frac{qE}{M}=qE=$ constant