Q. The mass of a proton is 1836 times that of an electron. An electron and a proton are projected into a uniform electric field in a direction perpendicular to the field with equal initial kinetic energies. Then
A) The electron trajectory is less curved than the proton trajectory
B) The proton trajectory is less curved than the electron trajectory
C) Both trajectories are equally curved
D) Both trajectories will be straight
Explanation
(c) $E = \frac{1}{2}mv^{2}$ or $v^{2} = 2E/m;$
If $E'$ is the intensity of electric field applied then $E^{'}q = mv^{2}/r$
or $r = mv^{2}/E'q$
or $r = \frac{m(2E/m)}{E^{'}q}$=$\frac{2}{q}\frac{E}{E^{'}}$
$ie,\ r \propto 1/q$
so $\frac{r_{e}}{r_{p}} = \frac{e}{e} = 1\ \ ie,\ r_{e} = r_{p}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.