An electron of mass ' $m$ ' and charge ' $q$ ' is accelerated from rest in a uniform electric field of…
An electron of mass ' $m$ ' and charge ' $q$ ' is accelerated from rest in a uniform electric field of strength ' $E$ '. The velocity acquired by the electron when it travels a distance ' $L$ ' is
$\sqrt{\frac{2 q E}{m L}}$
$\sqrt{\frac{2 E m}{q L}}$
$\sqrt{\frac{2 \mathrm{qEL}}{\mathrm{m}}}$
$\sqrt{\frac{\mathrm{qE}}{\mathrm{mL}}}$
Solution
Force on the electron $\mathrm{F}=\mathrm{qE}$
Work done by the force $\mathrm{W}=\mathrm{qEL}$
Work done is equal to gain in kinetic energy
$\begin{aligned}
& \therefore \frac{1}{2} \mathrm{mv}^2=\mathrm{qEL} \\
& \therefore \mathrm{v}=\sqrt{\frac{2 \mathrm{qEL}}{\mathrm{m}}}
\end{aligned}$