The formula
F = q · v · B · sin θ
| Symbol | Quantity | Unit |
|---|---|---|
| F | Magnetic force | N |
| q | Charge | C |
| v | Speed | m/s |
| B | Magnetic field | T |
| θ | Angle with the field | ° |
What it means
A magnetic field only pushes on charges that are moving, and only on the component of that motion across the field. The force is perpendicular to both the velocity and the field, which is what makes charged particles spiral.
How to work it out by hand
- Multiply the charge by its speed
- Multiply by the magnetic field strength
- Multiply by the sine of the angle between velocity and field
What is worth knowing
Because the force is always perpendicular to the motion, it changes direction without changing speed — and therefore does no work at all. That is why charged particles trapped in the Earth's magnetic field spiral along the field lines rather than being sped up or stopped, and it is what produces the auroras where those lines meet the atmosphere near the poles. Move exactly along the field and the sine is zero and so is the force. The same principle runs cyclotrons, mass spectrometers and the magnetic confinement in a fusion reactor.