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A charged ion of mass $$m$$ and charge $$q$$ is moving in circular path of radius $$r$$ in a plane at right angles to a magnetic field of strength $$B$$. Frequency of revolution of the particle is
The magnetic force provides the centripetal force, $$qvB = \frac{mv^2}{r}$$, so $$v = \frac{qBr}{m}$$. The time period is $$T = \frac{2\pi r}{v} = \frac{2\pi m}{qB}$$, and the frequency is $$\frac{1}{T} = \frac{qB}{2\pi m}$$.
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