Q. An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true?
A) Trajectory of electron is less curved
B) Trajectory of proton is less curved
C) Both trajectories are equally curved
D) Both move on straight line path
Explanation
(b) $E = \frac{1}{2}\ mv^{2}\ \ \ \ or\ \ \ \ \sqrt{2\ E/m};$
$r = \frac{mv}{Bq} = \frac{m}{Bq}\sqrt{2E/m}$
Or $r\ = \frac{\sqrt{2Em}}{Bq}\ \ \ \ \ \ or\ \ \ \ r \propto \ \sqrt{m};$
As , $m_{e} < m_{P};\ \ so,\ r_{e} < r_{P}$
Therefore, trajectory of proton is less curved
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.