Lorentz Force

Definition

The combined push on a charged particle from electric and magnetic fields — the force behind motors, auroras, and particle accelerators.

$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$

Symbol: $F$ · Unit: N

Technical definition

F = q(E + v × B): the electric part acts along E, the magnetic part perpendicular to both velocity and B. The magnetic component does no work (always perpendicular to motion) — it only bends trajectories.

Example

Auroras happen when solar-wind charges spiral along Earth's magnetic field — the v × B force curves their paths into the poles, where they slam into the atmosphere and glow.

Common confusion

Magnetic forces never change a particle's speed — only its direction. If a problem asks for the work done by a magnetic field, the answer is always zero; only electric fields (or the E part) do work.