Lorentz Force Calculator
The force on a charged particle moving through a magnetic field — and the radius and period of the circle it is bent into, which is how mass spectrometers, cyclotrons and the aurora all work.
A charge moving across a magnetic field feels a force qvB at right angles to both its velocity and the field.
How the lorentz force calculator works
A charge moving across a magnetic field feels a force qvB at right angles to both its velocity and the field. Because the force is always perpendicular to the motion it does no work: the particle keeps its speed and curves into a circle of radius mv/qB.
The period of that circle, 2πm/qB, does not depend on speed at all. That single fact is what makes a cyclotron possible.
Formula: F = q v B sin θ; r = m v / (q B); T = 2π m / (q B)
Worked examples
| Inputs | Force (N) | Note |
|---|---|---|
| A proton at 1,000 km/s in 0.5 T | 8.0109e-14 | a 2 cm circle |
| A stronger field | 3.2044e-13 | a quarter of the radius |
| Along the field | 0 | no force at all |
FAQFrequently asked questions
What is the Lorentz force?
The force on a charge from electric and magnetic fields. This page takes the magnetic part, qv × B, which is what bends a moving charge into a curve.
Why does the particle not speed up?
Because the force is always at right angles to the velocity, so it does no work. It changes direction only, which is why the path is a circle.
Why does the period not depend on speed?
A faster particle makes a bigger circle, and the two effects cancel exactly. The cyclotron exploits that: the same frequency accelerates the particle on every turn.
How does a mass spectrometer use this?
Ions of the same speed and charge curve by a radius proportional to their mass. Heavier ions land further along the detector.
What about the aurora?
Charged particles from the sun spiral along the Earth's field lines — the helix case here — and strike the atmosphere near the poles where the lines come down.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.