Question

An electron and a proton enters in a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is correct?

• 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

Answer 1

Answer: (B)

Charged particle enters in magnetic field perpendicularly it moves in circular path. Therequired centripetal force is provided by magnetic force.
$r=\frac{mv}{Bq}$
Kinetic energy of the particle
$K=\frac{1}{2}m{v}^2\Rightarrow mv=\sqrt{2mK}$
$r=\frac{\sqrt{2mK}}{qB}$
$r\propto \sqrt{m}$
$\frac{r_e}{r_p}=\sqrt{\frac{m_e}{m_p}}$
So, $m_e<m_p$
$r_e<r_p$
Trajectory of electron is more curved and trajectory of proton is less curved.