Question

An electron of mass $m_e$ initially at rest, moves through a certain distance in a uniform electric field in time $t_1.$ A proton of mass $m_p$, also initially at rest, takes time $t_2$ to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio $t_2/t_1$ is nearly equal to

• A. ${\left(\frac{m_p}{m_e}\right)}^{1/2}$
• B. ${\left(\frac{m_e}{m_p}\right)}^{1/2}$
• C. 1
• D. 1836

Answer 1

Answer: (A)

Force acting on a charged particle in a uniform electric field is given by $F=qE$
The acceleration imparted to the particle is
$a=\frac{qE}{m}$
Distance travelled by the particle in time $t$ is
$d=\frac{1}{2}a{t}^2=\frac{1}{2}\left(\frac{qE}{m}\right)t^2$
$(\because u=0)$
For the given problem, we have $d_p=d_e$
$\therefore \frac{t_p^2}{m_p}=\frac{t_e^2}{m_e}$ or
$\frac{t_p}{t_e}={\left(\frac{m_p}{m_e}\right)}^{1/2}$or
$\frac{t_2}{t_1}={\left(\frac{m_p}{m_e}\right)}^{1/2}\left(\because q_e=q_p\right)$