Question

An electron having charge $e$ and mass $m$ starts from the lower plate of two metallic plates separated by a distance $d$. If the potential difference between the plates is $V$, the time taken by the electron to reach the upper plate is given by

• A. $\sqrt{\frac{2 m d^{2}}{e V}}$
• B. $\sqrt{\frac{m d^{2}}{e V}}$
• C. $\sqrt{\frac{m d^{2}}{2 e V}}$
• D. $\frac{2 m d^{2}}{e V}$

Answer 1

Answer: (A)

$E=\frac{V}{d}, F=e E=e V / d$
$a=\frac{F}{m}=\frac{e V}{m d}$
$d=\frac{1}{2} a t^{2}$ or $t=\sqrt{\frac{2 d}{a}} $
or $ t=\sqrt{\frac{2 d m d}{e V}}=\sqrt{\frac{2 m d^{2}}{e V}}$