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  4. A proton, a deuteron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

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Q. A proton, a deuteron and an $\alpha$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

JEE MainJEE Main 2022Moving Charges and Magnetism

Solution:

$R =\frac{\sqrt{2 km }}{ qB } \propto \frac{\sqrt{ m }}{ q }$
$\frac{\sqrt{ m }}{ e }: \frac{\sqrt{2 m }}{ e }: \frac{\sqrt{4 m }}{2 e }$
$1: \sqrt{2}: 1$