Question

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

• 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)

The force on electron $=e E$
Due to motion, $F=m a$
$\therefore e E=m a$
$a=\frac{e E}{m}$
Distance fallen,
$h =u t+\frac{1}{2} a t^{2} $
$u =0 \Rightarrow h=\frac{1}{2} a t^{2} $
$h =\frac{1}{2}\left(\frac{e E}{m}\right) t^{2} $
$\therefore t =\sqrt{\frac{2 h m}{e E}}$