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 $F=q E$
The acceleration imparted to the particle is
$a=\frac{q E}{m}$
Distance travelled by the particle in time $t$ is
$d=\frac{1}{2} a t^{2}=\frac{1}{2}\left(\frac{q E}{m}\right) t^{2}$
$(\because u=0)$
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)$