Cyclotron Frequency
f = q · B / (2π · m)
Quick answer
This calculator solves f = q × B / (2π × m) for Frequency. With Charge 100 mC, Flux Density 0.5 T, Particle Mass 1 kg, the result is 0.007958 Hz. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A charged particle moving in a magnetic field circles at the cyclotron frequency, which depends only on the charge-to-mass ratio and the field strength—not on the particle’s speed or orbit radius. This frequency-independence of energy is what makes cyclotron particle accelerators and electron-cyclotron-resonance sources work, and it sets the resonance used in mass spectrometry.
Variables
- f — Cyclotron frequency (Hz)
- q — Particle charge (C)
- B — Magnetic flux density (T)
- m — Particle mass (kg)
Practical Notes
For an electron (q/m ≈ 1.76×10¹¹ C/kg), the cyclotron frequency is about 28 GHz per tesla. The orbit radius r = m·v/(q·B) grows with speed even though the frequency stays fixed.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Frequency | Hz | Hz, kHz, MHz, GHz |
| q | Charge | C | pC, nC, µC, mC, C |
| B | Flux Density | T | G, mT, T |
| m | Particle Mass | kg | kg, g, mg |
Step by step
- 1. What you know: Charge 100 mC, Flux Density 0.5 T, Particle Mass 1 kg
- 2. The relation: f = q × B / (2π × m)
- 3. Substitute: q = 100 mC, B = 0.5 T, m = 1 kg
- 4. Result: Frequency = 0.007958 Hz
Worked examples
Minimum range
Given: Charge 100 µC, Flux Density 10 G, Particle Mass 1 g
Result: Frequency = 1.59 × 10⁻⁵ Hz
Low range
Given: Charge 1 mC, Flux Density 10 mT, Particle Mass 10 g
Result: Frequency = 1.59 × 10⁻⁴ Hz
Typical
Given: Charge 100 mC, Flux Density 0.5 T, Particle Mass 1 kg
Result: Frequency = 0.007958 Hz
High range
Given: Charge 1 C, Flux Density 1.5 T, Particle Mass 100 kg
Result: Frequency = 0.002387 Hz
Maximum range
Given: Charge 10 C, Flux Density 15 T, Particle Mass 1000 kg
Result: Frequency = 0.02387 Hz
Solving for each variable
Solve for Frequency
Charge 100 µC, Flux Density 10 G, Particle Mass 1 g → 1.59 × 10⁻⁵ Hz
Solve for Charge
Frequency 5 Hz, Flux Density 10 G, Particle Mass 1 g → 31.42 C
Solve for Flux Density
Frequency 5 Hz, Charge 100 µC, Particle Mass 1 g → 314.2 T
Solve for Particle Mass
Frequency 5 Hz, Charge 100 µC, Flux Density 10 G → 0.003183 mg
How Frequency changes with Charge
| Charge (input) | Frequency (result) |
|---|---|
| 10 mC | 7.96 × 10⁻⁴ Hz |
| 25 mC | 0.001989 Hz |
| 50 mC | 0.003979 Hz |
| 75 mC | 0.005968 Hz |
| 100 mC | 0.007958 Hz |
| 150 mC | 0.01194 Hz |
| 0.2 C | 0.01592 Hz |
| 0.4 C | 0.03183 Hz |
| 0.7 C | 0.0557 Hz |
| 1 C | 0.07958 Hz |
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<p><a href="https://vbatpower.com/formulas/cyclotron-frequency/">Cyclotron Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Cyclotron Frequency?
Use f = q × B / (2π × m). With Charge 100 mC, Flux Density 0.5 T, Particle Mass 1 kg, Frequency works out to 0.007958 Hz.
What is the formula for Cyclotron Frequency?
The formula is f = q × B / (2π × m). A charged particle moving in a magnetic field circles at the cyclotron frequency, which depends only on the charge-to-mass ratio and the field strength—not on the particle’s speed or orbit radius.
How do you find Charge when you know the other values?
Rearrange for Charge: with Frequency 5 Hz, Flux Density 10 G, Particle Mass 1 g, Charge is 31.42 C.
How do you find Flux Density when you know the other values?
Rearrange for Flux Density: with Frequency 5 Hz, Charge 100 µC, Particle Mass 1 g, Flux Density is 314.2 T.
Related Concepts
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