# Ampère's law

Ampère's law
the law that a magnetic field induced by an electric current is, at any point, directly proportional to the product of the current intensity and the length of the current conductor, inversely proportional to the square of the distance between the point and the conductor, and perpendicular to the plane joining the point and the conductor.
[named after A. M. AMPÈRE]

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Law of electromagnetism that describes mathematically the magnetic force between two electric currents.

It was named after A.-M. Ampère, who discovered that such forces exist. If two currents flow in the same direction, the force between the two wires is attractive; if they flow in opposite directions, the force is repulsive. In each case, the force is directly proportional to the currents.

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one of the basic relations between electricity and magnetism, stating quantitatively the relation of a magnetic field to the electric current or changing electric field that produces it. The law is named in honour of André-Marie Ampère, who by 1825 had laid the foundation of electromagnetic theory. An alternative expression of the Biot-Savart law (q.v.), which also relates the magnetic field and the current that produces it, Ampère's law is generally stated formally in the language of calculus: the line integral of the magnetic field around an arbitrarily chosen path is proportional to the net electric current enclosed by the path. James Clerk Maxwell (Maxwell, James Clerk) is responsible for this mathematical formulation and for the extension of the law to include magnetic fields that arise without electric current, as between the plates of a capacitor, or condenser, in which the electric field changes with the periodic charging and discharging of the plates but in which no passage of electric charge occurs. Maxwell also showed that even in empty space a varying electric field is accompanied by a changing magnetic field. In this more general form, the so-called Ampère-Maxwell law is one of the four Maxwell equations that define electromagnetism.

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Universalium. 2010.

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