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  4. The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its :

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Q. The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its :

AIEEEAIEEE 2002Moving Charges and Magnetism

Solution:

In a circular motion in a uniform magnetic field, the necessary centripetal force to the charged particle is provided by the magnetic force, i.e.,
$\frac{m v^{2}}{r}=q v B$
or $r=\frac{m v}{q B}$
Thus, the time period $T$ is
$T=\frac{2 \pi r}{\nu}=\frac{2 \pi}{v}\left(\frac{m v}{q B}\right)=\frac{2 \pi m}{q B}$
So, T is independent of its speed.