Cyclotron Frequency Calculator

What Is Cyclotron Frequency?

Cyclotron frequency is the rate at which a charged particle orbits in a uniform magnetic field. It depends on charge-to-mass ratio and field strength, not on particle speed (non-relativistic limit).

Cyclotron Frequency Formula

$$f = \frac{qB}{2\pi m}$$

$q$ is particle charge in coulombs, $B$ is magnetic field in tesla, and $m$ is mass in kilograms. Angular frequency is $\omega = 2\pi f = qB/m$.

Example: a proton ($q = 1.602 \times 10^{-19}$ C, $m = 1.673 \times 10^{-27}$ kg) in 1 T field has $f \approx 15.2$ MHz.

Applications

Cyclotron frequency appears in particle accelerators, mass spectrometry, MRI physics, plasma confinement, and ion trap design.

Frequently Asked Questions

Why does mass matter?

Heavier particles orbit more slowly at the same charge and field. Mass spectrometers exploit different cyclotron frequencies to separate ions.

Does velocity affect cyclotron frequency?

In the classical non-relativistic limit, no. At very high speeds, relativistic corrections increase the effective mass.

What magnetic field units should I use?

Use tesla (T). 1 T = 10,000 gauss. Earth's field is about 25–65 µT.

Can I use this for electrons?

Yes. Use electron charge $1.602 \times 10^{-19}$ C and mass $9.109 \times 10^{-31}$ kg for much higher frequencies at the same field.

What is the relationship to Larmor radius?

Orbital radius $r = mv/(qB)$ depends on speed, but frequency $f = qB/(2\pi m)$ does not in the classical limit.

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Cyclotron Frequency Calculator

What Is Cyclotron Frequency?

Cyclotron Frequency Formula

Applications

Frequently Asked Questions

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