Question

A particle of mass $M$ and charge $q$ is released from rest in a region of uniform electric field magnitude $E$. After a time $t$, the distance travelled 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

Answer: (A)

remains constant with time $t$

Given, mass of the particle $=M$
Charge on the particle $=q$
Electric field $=E$
Initial velocity, $u=0$
$\therefore$ Acceleration, $a=\frac{F}{M}=\frac{qE}{M}$
$\therefore$ Distance travelled in electric field
$S=ut+\frac{1}{2}a{t}^2$
$S=\frac{1}{2}\left(\frac{qE}{M}\right)t^2$
Also, Kinetic energy $T=\frac{1}{2}M{\left(\frac{qEt}{M}\right)}^2$
So, $\frac{T}{S}=\frac{\frac{1}{2}M{\left(\frac{qEt}{M}\right)}^2}{\frac{1}{2}\left(\frac{qE}{M}\right)t^2}=qE$
$\Rightarrow$ Ratio of $\frac{T}{S}$ remains constant with time $t$