Question

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

Answer 1

Answer: (B)

Trajectory of proton is less curved

Radius of circular path traced by a charged particle $R=\frac{mv}{Bq}$

Kinetic energy of charged particle $K=\frac{1}{2}m{v}^2$

$⟹mv=\sqrt{2Km}$

$\therefore$ $R=\frac{\sqrt{2Km}}{Bq}$

Thus $R\propto \sqrt{m}$ (for same $K$ and $q$)

Since mass of proton is more than that of electron i.e. $m_p>m_e$ and both have same magnitude of charge.

$⟹R_p>R_e$

So, trajectory of proton is less curved.