Question

An electron and proton enter a magnetic Held 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: (A)

Trajectory of electron is less curved

Answer 2

When a charged particle enters a magnetic field perpendicularly, it moves on a circular path. The required centripetal force is provided by magnetic force. ie, Magnetic force= Centripetal force or $q v B=\frac{m v^{2}}{r}$ $\therefore r=\frac{m v}{q B} \ldots(i)$ Now kinetic energy of the particle $K=\frac{1}{2} m v^{2}$ $\Rightarrow m v=\sqrt{2 m K}$ Therefore, E (i) becomes $r=\frac{\sqrt{2 m K}}{q B}$ or $r \propto \sqrt{m}$ $\therefore \frac{r_{e}}{r_{p}}=\sqrt{\frac{m_{e}}{m_{p}}}$ As $m_{e} < m_{p} ; s o, r_{e} < r_{p}$ Hence, trajectory of electron is less curved.