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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:

JamiaJamia 2005

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}=qvB $ $ r=\frac{mv}{qB} $ Thus, the time period T is $ T=\frac{2\pi r}{v} $ $ =\frac{2\pi m}{qB} $ So, Tis independent of its speed.