Q. Two ions having masses in the ratio 1 : 1 and charges 1 : 2 are projected into uniform magnetic field perpendicular to the field with speeds in the ratio 2 : 3. The ratio of the ratio of circular paths along which the two particles move is
A) 4 : 3
B) 2 : 3
C) 3 : 1
D) 1 : 4
Explanation
(a) $m_{1}\ :m_{2} = 1\ :1$
$q_{1}:q_{2} = 1\ :2$
$v_{1}:v_{2} = 2\ :3$
Radius of path of charged particle moving in uniform magnetic field,
$r = \frac{mv}{Bq}$
$\therefore\frac{r_{1}}{r_{2}} = \left( \frac{m_{1}}{m_{2}} \right)\ \left( \frac{v_{1}}{v_{2}} \right)\ \times \left( \frac{q_{2}}{q_{1}} \right) = \frac{1}{1} \times \frac{2}{3} \times \frac{2}{1} = \frac{4}{3}$
$r_{1}\ :r_{2} = 4\ :3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.