Question

A particle with specific charge 's' starts from rest in a region where the electric field has a constant directlon, but whose magnitude increases linearly with time. The particle acquires a velocity v in time t second. Then:

• A. $v\propto s$
• B. $\vee \propto \sqrt{s}$
• C. $v\propto t$
• D. $v\propto t^2$

Answer 1

Answer: (A), (D)

The correct options are
A $v\propto s$
D $v\propto t^2$

$E=\alpha t,$ where $\alpha$ is a constant.

$F=QE$

Acceleration, $a=\frac{F}{m}=\frac{QE}{m}$

$\frac{QE}{m}=sE=\alpha st$

$\therefore a=\frac{dv}{dt}=\alpha st$ or $v=\frac{1}{2}\alpha s{t}^2$

$\therefore v\alpha s$ and $v\alpha t^2$