The Lorentz Force
A magnetic field can push on a moving charge, but only sideways — perpendicular to both its velocity and the field itself. This sideways push never speeds the charge up or slows it down; it only bends the path, curving it into a circle if the field stays constant.
The formula
F = q · v · B
- F — force (N): the sideways magnetic push on the charge
- q — charge (C): the amount of electric charge carried by the particle
- v — velocity (m/s): how fast the charge is moving, here perpendicular to the field
- B — magnetic field (T): the strength of the magnetic field the charge moves through
Worked example
A charged particle with a charge of 2 coulombs moves at 3 meters per second, perpendicular to a magnetic field of 5 tesla. What force does it feel?
- q = 2 C
- v = 3 m/s
- B = 5 T
- F = q · v · B
- F = 2 C · 3 m/s · 5 T
F = 30 N
Test yourself
The same 2 coulomb charge now moves at 3 meters per second through a stronger 10 tesla field. What is the force on it?
- 30 N
- 15 N
- Correct answer: 60 N
Right! Doubling the field doubles the force: 2 C × 3 m/s × 10 T = 60 N.
A positive charge moves to the right through a magnetic field pointing into the page. Which way does the magnetic force push it?
- Correct answer: Upward
- Downward
- Forward, in the same direction it's already moving
Correct! Using the right-hand rule, a rightward-moving positive charge in a field pointing into the page feels a force pushing it upward.
Where you see this
An old CRT television steered its electron beam with magnetic fields, painting the screen by bending charged particles thousands of times a second. The northern lights are the same physics at planetary scale: charged particles from the sun spiral along Earth's magnetic field lines, glowing as they curve.
Common mistakes
The key subtlety is that the magnetic force does no work: F = q · v · B pushes perpendicular to the velocity, so it can bend a path but never speed the charge up or slow it down. Getting direction wrong is the other slip — the force is perpendicular to both the velocity and the field (right hand: fingers along the velocity, curl toward the field, thumb along the force). A positive charge at 3 m/s crossing a 10 T field feels 2 C × 3 m/s × 10 T = 60 N sideways.
How it connects
Currents make fields and fields push moving charges — the two halves of electromagnetism's feedback pair, one lesson apart. Faraday's law, next, adds the third: a changing field creates a voltage that drives a current all by itself. This sideways, speed-preserving push is why motors spin and why charged particles run in circles in accelerators.