cyclotron frequency

Question

Cyclotron frequency for charge q, mass m in magnetic field B is:

RankGuru · Accepted Answer

When a charge enters a magnetic field perpendicularly ($v \perp B$), it moves in a circle. The magnetic force provides the centripetal force:
$qvB = \frac{mv^2}{r} \implies v/r = \frac{qB}{m}$
- The **angular frequency** $\omega = v/r = \frac{qB}{m}$.
- The frequency $f = \frac{\omega}{2\pi} = \frac{qB}{2\pi m}$.
- Note: The frequency is **independent** of the speed $v$ and radius $r$ of the particle (within non-relativistic limits).

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Cyclotron angular frequency ω for charge q, mass m in magnetic field B?