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. $\sqrt{\frac{2m{d}^2}{eV}}$
• B. $\sqrt{\frac{m{d}^2}{eV}}$
• C. $\sqrt{\frac{m{d}^2}{2eV}}$
• D. $\frac{2m{d}^2}{eV}$

Answer 1

The correct option is A $\sqrt{\frac{2m{d}^2}{eV}}$

$E=\frac{V}{d}$,

force on the electron is $F=eE=eV/d$

$a=\frac{F}{m}=\frac{eV}{md}$

$d=u_{0}t+\frac{1}{2}a{t}^2⟹t=\sqrt{\frac{2d}{a}}$

but initially velocity is zero, so $u_0=0$

$d=u_{0}t+\frac{1}{2}a{t}^2=\frac{1}{2}a{t}^2=\frac{eV{t}^2}{2md}$

or $t=\sqrt{\frac{2dmd}{eV}}=\sqrt{\frac{2m{d}^2}{eV}}$