Q. Which of the following particles will describe the smallest circle when projected with the same velocity perpendicular to the magnetic field?
A) Electron
B) Proton
C) $\alpha - particle$
D) Deuteron
Explanation
(a) In this case path of charged particle is circular and magnetic force provides the necessary centripetal force $ie,\ Bqv = \frac{mv^{2}}{r}$
$\Rightarrow \ \ Radius\ of\ path\ r = \frac{mv}{Bq}$
Since $v\ and\ B$ will remain same, so $r \propto \frac{m}{q}.$ The ratio is least for electron, therefore, it will describe the smallest circle.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.