Lorentz Force
Compute the full electromagnetic force on a charged particle moving through electric and magnetic fields, as a 3D vector. Add a mass to get the acceleration, the cyclotron radius and frequency, and a simulated trajectory.
What is the Lorentz Force?
A charge q feels two forces. The electric force qE pushes along the field, whether the charge moves or not. The magnetic force qv×B only acts on moving charges and is always perpendicular to both the velocity and the field.
Because the magnetic force is perpendicular to the motion it never changes the particle’s speed — it only bends its path, into a circle or a helix. This principle runs electric motors, mass spectrometers, particle accelerators and the old CRT television.
Live 3D View
directionsTypical Magnetic Fields
| Source | B |
|---|---|
| Earth’s magnetic field | 25–65 µT |
| Fridge magnet | ~5 mT |
| Neodymium magnet surface | ~1.2 T |
| Hospital MRI scanner | 1.5–3 T |
| LHC bending magnets | 8.3 T |
| Magnetar (neutron star) | 109–1011 T |
| e = 1.602176634×10−19 C · 1 T = 1 N/(A·m) = 104 gauss | |
Key Applications
Your thumb then points along v×B — the force on a positive charge. For electrons, reverse it.
The orbit frequency does not depend on the speed — the idea behind the cyclotron accelerator and mass spectrometers, where r reveals the mass.
Crossed E and B fields cancel exactly for one speed. Only particles with v = E/B pass straight through — independent of charge and mass.
Sources & Verification
- D. J. Griffiths, Introduction to Electrodynamics, 4th ed., Pearson, 2013 — Ch. 5 (Magnetostatics).
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 28 (Magnetic Fields).
- E. Tiesinga, P. J. Mohr, D. B. Newell & B. N. Taylor, “CODATA recommended values of the fundamental physical constants: 2018”, Reviews of Modern Physics 93, 025010 (2021) — values of the constants used.