Question

An electron of mass $m$, charge $e$ falls through a distance $h$ meter in a uniform electric field $E$.

Then, time of fall is:

• A. $t=\sqrt{\frac{2hm}{eE}}$
• B. $t=\frac{2hm}{eE}$
• C. $t=\sqrt{\frac{2eE}{hm}}$
• D. $t=\frac{2eE}{hm}$

Answer 1

Answer: (A)

$t=\sqrt{\frac{2hm}{eE}}$

Electrostatic force acting on the charge, $F=eE$

$\therefore$ Acceleration of charge, $a=\frac{F}{m}=\frac{eE}{m}$

Initial velocity of charge, $u=0$ m/s

Using: $S=ut+\frac{1}{2}a{t}^2$

$\therefore$ $h=0+\frac{1}{2}\times \frac{eE}{m}{t}^2$ $⟹t=\sqrt{\frac{2hm}{eE}}$