Question

A proton of mass $m$ charge $e$ is released from rest in a uniform electric field of strength $E$. The time taken by it to travel a distance $d$ in the field is :

• A. $\sqrt{\frac{2de}{mE}}$
• B. $\sqrt{\frac{2dm}{Ee}}$
• C. $\sqrt{\frac{2dE}{me}}$
• D. $\sqrt{\frac{2Ee}{dm}}$

Answer 1

The correct option is B $\sqrt{\frac{2dm}{Ee}}$

Force acting on proton $=qE$

Acceleration $a=\frac{qE}{m}$

Given proton is initially at rest $u=0$

we know $X=ut+\frac{1}{2}a{t}^2$

$\Rightarrow d=\frac{1}{2}\cdot \frac{Eq}{m}{t}^2$

$\Rightarrow t=\sqrt{\frac{2md}{Eq}}$

$\Rightarrow t=\sqrt{\frac{2md}{Ee}}$ ( q $=$ e for a proton)