This article examines the force deduced by Ampère (1775–1826). In 1820 Oersted conducted his revolutionary experiment: a current-carrying wire capable of deflecting a compass needle. To explain this phenomenon Ampère presented two crucial hypotheses: he postulated the existence of forces between current-carrying conductors and suggested that electric currents existed not only in conductive wires, but also inside magnets and even within the Earth. To deduce his force Ampère developed his famous cases of equilibrium in which a mobile circuit is kept at rest between two opposing forces or between two opposing torques. In 1822 Ampère obtained his final expression, a central force consistent with Newton’s third law of motion. According to Ampère’s force, the action between two current elements is proportional to the product of their intensities, to the product of their infinitesimal lengths, and varies inversely with the square of their distance. Furthermore, this force depends on three angles. According to Maxwell, Ampère’s force should always remain the most important formula of electrodynamics. However, despite this positive evaluation, Ampère’s force disappeared from modern textbooks, being replaced by Grassmann’s theoretical force from 1845, which does not comply with Newton’s third law. In 1822 Ampère predicted the existence of longitudinal repulsive forces between two collinear and parallel elements with currents in the same direction. This force should not exist according to Grassmann’s law. Ampère created the bridge experiment to test this prediction and it was successful. Maxwell, while aware of both expressions (Ampère’s and Grassmann’s forces), expressly preferred Ampère’s force.
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