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In magnetostatics, the force of attraction or repulsion between two current-carrying wires (see first figure below) is often called Ampère's force law. The physical origin of this force is that each wire generates a magnetic field , following the Biot–Savart law , and the other wire experiences a magnetic force as a consequence, following ...
Ampère's force law describes the experimentally-derived fact that, for two thin, straight, stationary, parallel wires, a distance r apart, in each of which a current I flows, the force per unit length, F m /L, that one wire exerts upon the other in the vacuum of free space would be given by .
[54]: 189–192 Later, Franz Ernst Neumann proved that, for a moving conductor in a magnetic field, induction is a consequence of Ampère's force law. [54]: 222 In the process, he introduced the magnetic vector potential, which was later shown to be equivalent to the underlying mechanism proposed by Faraday. [54]: 225
Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary.
For alternating currents and point charges, the different representations of Ampere's force law are not equivalent. Maxwell was familiar with Weber's electrodynamics and mentioned it positively. [11] Nevertheless, he decided to build his theory on the Biot-Savart law by generalizing it to cases where the conductor loops contain discontinuities.
André-Marie Ampère (UK: / ˈ æ m p ɛər /, US: / ˈ æ m p ɪər /; [1] French: [ɑ̃dʁe maʁi ɑ̃pɛʁ]; 20 January 1775 – 10 June 1836) [2] was a French physicist and mathematician who was one of the founders of the science of classical electromagnetism, which he referred to as electrodynamics.
The four equations we use today appeared separately in Maxwell's 1861 paper, On Physical Lines of Force: Equation (56) in Maxwell's 1861 paper is Gauss's law for magnetism, ∇ • B = 0. Equation (112) is Ampère's circuital law, with Maxwell's addition of displacement current.
Ampère's circuital law; Ampère's force law; Amrom Harry Katz; Amsterdam Density Functional; An Album of Fluid Motion; An Elementary Treatise on Electricity; An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism; An Exceptionally Simple Theory of Everything