Question

An electron of mass '$m$' and charge '$q$' is accelerated from rest in a uniform electric field of strength '$E$'. The velocity acquired by it as it travels a distance '$l$' is :

• A. ${\left[\frac{2Eql}{m}\right]}^{\frac{1}{2}}$
• B. ${\left[\frac{2Eq}{ml}\right]}^{\frac{1}{2}}$
• C. ${\left[\frac{2Em}{ql}\right]}^{\frac{1}{2}}$
• D. ${\left[\frac{Eq}{ml}\right]}^{\frac{1}{2}}$

Answer 1

The correct option is A ${\left[\frac{2Eql}{m}\right]}^{\frac{1}{2}}$

Electrostatic force acting on the electron $F=qE$

Thus acceleration of the electron $a=\frac{F}{m}=\frac{qE}{m}$

Initial speed of the electron $u=0$

Using $v^2-u^2=2aS$

where $S$ is the distance traveled.

$\therefore$ $v^2-0=2\frac{qE}{m}l$

$⟹$ $v=[\frac{2qEl}{m}{]}^{1/2}$