Physics
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Cyclotron Frequency Calculator.
Calculate non-relativistic cyclotron frequency in a uniform magnetic field.
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Results update as you type.
Results update automatically as you type.
This page applies only the stated idealized equation and explicit inputs; verify specialized engineering, medical, or safety decisions against applicable standards.
Use Cases
Physics Education and Demonstrations
Helps students and educators quickly compute cyclotron frequency for textbook problems or lab setups, reinforcing the relationship between charge, magnetic field, and mass.
Example: Calculate the frequency for a proton (charge 1.602e-19 C, mass 1.673e-27 kg) in a 0.5 T field.
Particle Accelerator Design
Assists engineers and physicists in estimating the operating frequency for cyclotrons or similar devices, aiding in initial design and parameter checks.
Example: Determine the frequency needed for a carbon ion in a 2 T magnetic field.
Frequently Asked Questions
- What is cyclotron frequency?
- Cyclotron frequency is the rate at which a charged particle orbits in a uniform magnetic field, given by f = qB/(2πm). It depends on the particle's charge, the magnetic field strength, and the particle's mass.
- What units are used in this calculator?
- The calculator uses SI units: charge in coulombs (C), magnetic field in teslas (T), and mass in kilograms (kg). The result is the frequency in hertz (Hz).
- Does this calculator account for relativistic effects?
- No, it is designed for non-relativistic speeds. For particles moving at a significant fraction of the speed of light, relativistic corrections are needed, which are not included here.
Tips & Common Mistakes
Tips
- Ensure all inputs are in SI units: charge in coulombs, magnetic field in teslas, and mass in kilograms, to get the frequency in hertz.
- For particles like electrons or protons, use their known charge and mass values (e.g., electron: 1.602e-19 C, 9.109e-31 kg).
- Remember that the cyclotron frequency is independent of the particle's speed (as long as it's non-relativistic) and the radius of its orbit.
- Double-check the sign of the charge: the frequency is positive for positive charges and negative for negative charges, indicating the direction of rotation.
Common Mistakes to Avoid
- Using grams or atomic mass units instead of kilograms for mass, leading to incorrect frequency values.
- Forgetting to convert magnetic field from gauss to tesla (1 T = 10,000 G).
- Using the formula for angular frequency (ω = qB/m) instead of the cyclotron frequency (f = qB/(2πm)), which differs by a factor of 2π.
Last updated: August 13, 2026