Q. A proton and a deutron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field $B$. For motion of proton and deuteron on circular path of radius $R_{P}$ and $R_{d}$ respectively, the correct statement is
A) $R_{d} = \sqrt{2}\ R_{p}$
B) $R_{d} = R_{p}/\sqrt{2}$
C) $R_{d} = \ R_{p}$
D) $R_{d} = 2R_{p}$
Explanation
(a) $\frac{mv^{2}}{R} = qvB.$ For proton $R_{p} = \frac{mv}{qB} = \frac{\sqrt{2m_{p}E}}{qB}$
and for deuteron $R_{d} = \frac{\sqrt{2m_{d}E}}{qB}$
$\Rightarrow \frac{R_{d}}{R_{p}} = \sqrt{\frac{m_{d}}{m_{p}}} = \sqrt{2} \Rightarrow R_{d} = \sqrt{2}R_{p}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.