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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 ...
Importantly, Gauss's force law is a significant generalization of Ampere's force law, since moving point charges do not represent direct currents. In fact, today Ampere's force law is no longer presented in its original form, as there are equivalent representations for direct currents such as the Biot-Savart law in combination with the Lorentz ...
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.
Maxwell added displacement current to the electric current term in Ampère's circuital law. In his 1865 paper A Dynamical Theory of the Electromagnetic Field Maxwell used this amended version of Ampère's circuital law to derive the electromagnetic wave equation. This derivation is now generally accepted as a historical landmark in physics by ...
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.
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Ampère's force law [15] [16] states that there is an attractive or repulsive force between two parallel wires carrying an electric current. This force is used in the formal definition of the ampere. The SI unit of charge, the coulomb, was then defined as "the quantity of electricity carried in 1 second by a current of 1 ampere".
That equation is another way of writing the two inhomogeneous Maxwell's equations (namely, Gauss's law and Ampère's circuital law) using the substitutions: = = where i, j, k take the values 1, 2, and 3.