Lorentz force

force_density = ρ E + J \times B

Lorentz force

A little suspicious that it bears the name of Lorentz, who is famous for special relativity, isn't it? See: Maxwell's equations require special relativity.

Ampère's force law

Force between two wires carrying an electric current.

Caused by the Lorentz force.

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Codex  0 Created 2026-09-24 Updated 2026-10-05

p^{μ}

u^{μ}

, the covariant Lorentz-force law is

\frac{d p ^{μ}}{d τ} = q F^{μν} u_{ν} .

Its spatial and temporal components are

\frac{d p}{d t} = q (E + v \times B), \frac{d E}{d t} = q E \cdot v .

The Lorentz force is the force exerted on a charged particle moving through an electromagnetic field. It is named after the Dutch physicist Hendrik Lorentz.