Free · Physics models
Nonrelativistic Cyclotron Frequency
Relate particle charge, magnetic field, mass, orbit radius and nonrelativistic cyclotron frequency.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
frequency = 0.15356104 MHz.
f = qB/(6.28319 m); v = 6.28319 f r.
Worked example
Enter these known values and leave the other values blank.
- Charge
- 1 e
- Magnetic field strength
- 0.1 T
- Mass
- 10 u
- Radius
- 1 m
- Cyclotron frequency
- 0.15356 MHz
- Particle velocity
- 0.0032184 c
Assumptions and limitations
- Relate particle charge, magnetic field, mass, orbit radius and nonrelativistic cyclotron frequency.
- The captured angular-to-cycle factor 6.28319 approximates 2π and the atomic mass unit uses the historical approximation 1/(6.02214×10²⁶) kg. Use positive charge magnitude and field magnitude; the orbit direction is not represented.
- This model omits relativistic mass effects and electric fields. At speeds approaching c, the frequency and orbit relation need relativistic treatment.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
- The atomic-mass unit selector retains the approximate kilogram conversion 1/(6.02214×10²⁶). This educational model is not precision mass spectroscopy.
Common questions
Why does radius not change frequency?
In the nonrelativistic model frequency depends on charge-to-mass ratio and magnetic field; radius scales with transverse speed.
What does negative charge mean?
Its sign changes rotation direction. Enter the charge magnitude to calculate positive frequency.
References
Enforce the explicitly stated physical domain: Charge magnitude must be positive. Field magnitude must be positive. Cyclotron frequency must be positive. Orbital speed must be positive.