Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6 : 5

Question

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6 : 5 and their respective masses ratio is 9 : 4 . Then, the ratio of their charges will be

TestHub · Accepted Answer

Radius of charged particle moving in circular path $R = \frac{\sqrt{2 m K}}{q B}$ , here, $B$ is magnetic field and $K$ is kinetic energy.
So, $q = \frac{\sqrt{2 m K}}{R B}$
Now, ratio of the charges is $\frac{q_{1}}{q_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} \times \frac{R_{2}}{R_{1}} = \sqrt{\frac{9}{4}} \times \frac{5}{6} = \frac{5}{4}$

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