cyclotron frequency

Question

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

RankGuru · Accepted Answer

1. **Force Balance**: The magnetic force ($qvB$) provides the centripetal force ($mv^2/r$) for circular motion.
   - $qvB = \frac{mv^2}{r} \implies \frac{v}{r} = \frac{qB}{m}$.
2. **Definitions**: Angular frequency $\omega$ is defined as $v/r$.
3. **Substitute**: $\omega = \frac{qB}{m}$.
4. **Frequency ($f$)**: Note that $f = \frac{\omega}{2\pi} = \frac{qB}{2\pi m}$.
5. **Key Property**: The frequency is independent of the speed or radius of the particle.

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