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Cyclotron frequency
Intermediate
Frequency is independent of speed.
f = qB/2πmf = qB/(2πm), independent of speed and radius, which is why cyclotrons work with a fixed-frequency electric field.
Proton in 1 T: 15.2 MHz.
Relativity breaks this at high energies.
In more detail
The cyclotron frequency f = qB/(2πm) is the frequency of circular motion of a charged particle in a magnetic field. It does not depend on the speed for non-relativistic particles.
Real-world uses
- Cyclotrons are designed around a fixed frequency for acceleration.
- Mass spectrometry uses cyclotron resonance to identify ions.
- Cyclotrons accelerate protons in a fixed magnetic field, using an oscillating electric field tuned to the cyclotron frequency.
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Frequently asked questions
Why is the frequency independent of speed?
Because faster particles move in larger circles, so the time per revolution remains the same.
Does it matter for light particles?
Yes, lighter particles have higher cyclotron frequencies.
Why does the frequency not depend on speed?
For non-relativistic speeds, a faster particle moves in a larger circle, so it takes the same time for each turn.
Related topics in Magnetism & Induction
Earth's magnetic field · Magnetic force on a moving charge · Circular motion in B field · Helical motion · Velocity selector · Mass spectrometer