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

Answer 1

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

Let the acceleration of the electron be $a$ and its mass be $m$

The coulomb force helps the electron to accelerate and thus attain velocity $\left(v\right)$.

$\therefore$ $F_{coulomb}=ma$

$qE=ma$$⟹a=\frac{qE}{m}$ ........(1)

Let the velocity of the electron after travelling a distance $l$ be $v$.

Also the electron is at rest initially, i.e $u=0$

Using: $v^2-u^2=2al$

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

$⟹v=[\frac{2qEl}{m}{]}^{1/2}$