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  4. A proton and a deuteron with the same initial kinetic energy enter a magnetic field in a direction perpendicular to the direction of the field. The ratio of the radii of the circular trajectories described by them is

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Q. A proton and a deuteron with the same initial kinetic energy enter a magnetic field in a direction perpendicular to the direction of the field. The ratio of the radii of the circular trajectories described by them is

NTA AbhyasNTA Abhyas 2022

Solution:

For a moving charge in a perpendicular magnetic field,
$\frac{m v^{2}}{r}=Bqv$
$\Rightarrow \, \, r = \frac{m v}{B q} = \frac{p}{B q} = \frac{\sqrt{2 m K}}{q B}$
$\frac{r_{p}}{r_{d}}=\sqrt{\frac{m_{p}}{m_{d}}}= \, \sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$