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Cyclotron Frequency, Angular Frequency, and Period — result sheet
Calculate the angular frequency, ordinary frequency, and period of a signed charged particle in a positive magnetic field.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Cyclotron angular frequency is omega_c = |q|B/m; ordinary frequency is f_c = omega_c/(2 pi); period is T_c = 2 pi m/(|q|B).
This calculator applies the nonrelativistic uniform-field cyclotron relation to a signed charge, positive magnetic field, and positive mass. It returns angular frequency in rad/s, frequency in Hz, and period in seconds; q = 0 and any non-finite derived result are rejected.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Signed charge — C; Finite signed charge; zero is excluded by the cyclotron model.; minimum -1.0E-6; maximum 1.0E-6
- Magnetic field — T; Finite positive uniform magnetic-field magnitude in teslas.; minimum 1.0E-12; maximum 1000000
- Particle mass — kg; Finite positive particle mass in kilograms.; minimum 1.0E-32; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Signed charge | -1.602176634E-19 |
| Magnetic field | 1 |
| Particle mass | 9.1093837015E-31 |
An electron-mass charge at 1 T has an ideal angular frequency near 1.7588e11 rad/s, frequency near 2.7985e10 Hz, and period near 3.573e-11 s.
Assumptions and limits
- Charge is a finite signed value in coulombs and must be nonzero; its sign affects gyration direction but not the returned frequency magnitudes.
- Magnetic field is a finite positive magnitude in teslas and is treated as uniform and perpendicular to the ideal circular motion.
- Mass is a finite positive inertial mass in kilograms, and the particle speed is low enough for the nonrelativistic relation to apply.
- Electric fields, radiation, collisions, relativistic mass effects, field gradients, orbit geometry, equipment, and safety decisions are outside the calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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