Ampère's force law

Ampère's force law describes the magnetic force between current-carrying conductors, traditionally as a force between infinitesimal current elements. It helped establish electrodynamics as a quantitative theory.

Ampère's circuital force law: A mathematical formulation of the force between current elements, including their separation and orientation. This is the specific force law whose differential expression underlies Ampère's conductor-force calculations.
André-Marie Ampère: A French physicist and mathematician who founded mathematical electrodynamics. He formulated the force law from experiments on current-carrying conductors.
Ampère's force law for electrodynamics: A force-based formulation of electrodynamics in which currents interact directly at a distance. It contrasts with field-based formulations that describe forces through intervening fields.
Ampere: The SI base unit of electric current, symbol A. The unit is named for Ampère, whose force experiments informed historical current measurement.
Biot–Savart law: A law giving the magnetic field produced by a steady electric current. Its field for one conductor can be combined with the magnetic force on another.
Ørsted's experiment: Hans Christian Ørsted's 1820 demonstration that an electric current deflects a magnetic compass needle. It prompted Ampère to investigate forces and interactions between electric currents.
Maxwell's equations: A set of equations describing how electric and magnetic fields are generated and evolve. They recast electromagnetic interactions in terms of fields rather than direct current-element forces.
Current balance: An instrument that measures electric current by balancing magnetic forces between conductors. It turns the force between current-carrying wires into a method of measuring current.
Lorentz force: The force on a charged particle due to electromagnetic fields. It provides the modern field-based account of magnetic forces on moving charges.
Ampère's electrodynamics: The nineteenth-century theory describing interactions among electric currents and magnets. The force law formed a central part of Ampère's broader electrodynamic theory.

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