SACE Stage 2 Physics — Electricity & Magnetism 2.4

Magnetism from Relativity

A current-carrying wire is electrically neutral in the lab — yet a test charge moving alongside it feels a force. Hop into the test charge's frame: the moving ion lattice contracts, the now-stationary electrons spread out, and the wire picks up a net charge. The magnetic force in the lab is just an electric force in disguise. Drift speeds here are exaggerated so length contraction is visible.

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Reference frame

Drift speed β = v/c

Test charge

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Lorentz factor γ —

Linear charge density

+ions—

−electrons—

net—

Force on test charge —

Lab frame: ions and electrons have equal and opposite line densities, so the wire is neutral. The drifting electrons make a current, which produces a magnetic field. The test charge moves through that field and feels F = qv×B.