Estimate gyroradius using flexible particle and unit settings. View cyclotron frequency and period in seconds. Download a clean report file for your lab notes.
| Scenario | Particle | B | Method | Inputs | Notes |
|---|---|---|---|---|---|
| 1 | Proton | 50 µT | v⊥ | v⊥ = 1.0×106 m/s | Earth‑like field scale |
| 2 | Electron | 0.01 T | v + θ | v = 3.0×106 m/s, θ = 60° | Strong lab magnet |
| 3 | Alpha (He²⁺) | 1 mT | Ek + θ | Ek = 100 keV, θ = 90° | Energy‑based input |
A charged particle in a uniform magnetic field follows circular motion for its perpendicular velocity component. The gyroradius is:
Here, v⊥ = v·sinθ, where θ is the pitch angle between velocity and the field direction. For low speeds, set γ = 1.
The gyroradius (Larmor radius) is the orbit radius of a charged particle around magnetic field lines caused by the perpendicular velocity component. It measures magnetization: small rg supports guiding‑center motion, while large rg implies weak control by the field and larger cross‑field excursions.
In SI units rg = (γ m v⊥)/(|q| B). It scales linearly with mass and v⊥, and inversely with |q| and B. This calculator supports Tesla or Gauss for B, kg or amu for mass, and Coulombs or elementary charges for q.
Pitch angle θ is measured between the velocity vector and the magnetic field direction. The perpendicular component is v⊥ = v·sinθ, so θ near 0° produces negligible gyration, while θ near 90° maximizes it. Energy and speed modes both use θ to map your inputs to v⊥.
Cyclotron motion sets the rotation rate: fc = |q|B/(2πγ m) and Tc = 1/fc. For an electron in B = 0.01 T with γ≈1, fc ≈ 2.8×108 Hz and Tc ≈ 3.6 ns, useful for resonance planning.
Energy inputs are common in plasma and beam work. Non‑relativistically, v = √(2Ek/m), so a 1 keV proton has v≈4.4×105 m/s. At MeV energies, γ exceeds 1 and the speed approaches c; enabling the relativistic option prevents underestimating rg and overestimating ωc.
Environmental comparison helps interpretation. In an Earth-like field B≈50 µT, a proton with v⊥ = 1×106 m/s has rg≈2.1×102 m. In a 1 T lab magnet, the same case gives rg≈1×10−2 m, showing how stronger fields shrink orbits.
Relativity scales both radius and frequency through γ. At v = 0.8c, γ≈1.67, so rg grows by about 67% versus γ=1, while fc drops by the same factor. This matters for electrons and beams.
Check scaling: doubling B halves rg, doubling v⊥ doubles rg. If θ drives v⊥ toward zero, rg should approach zero. These checks reveal unit mistakes and keep comparisons consistent.
The gyroradius is the radius of the circular motion a charged particle executes around magnetic field lines due to its perpendicular velocity component in a uniform magnetic field.
The magnetic force is perpendicular to velocity and field. The parallel component produces no curvature, so only the perpendicular component drives circular motion and sets the orbit radius.
Enable it when speeds approach a significant fraction of light speed, or when energies are high enough that γ differs from 1, especially for electrons in strong fields.
Pitch angle θ is measured between the particle’s velocity vector and the magnetic field direction. The calculator uses v⊥ = v·sinθ and accepts degrees or radians.
Gyroradius is inversely proportional to magnetic field strength. Doubling B halves rg, while reducing B increases orbit size and reduces magnetization strength.
Yes. Choose Custom particle, select amu for mass, and enter the ion’s mass number approximation. Then specify charge in elementary charges for convenience.
The radius depends on the magnitude of the Lorentz force, which uses |q|. The sign of charge changes rotation direction, not the size of rg.
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