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In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law) [1] relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 published paper "On Physical Lines of Force". [2]
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 ...
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 ...
However, the law also applies to infinitely long wires (this concept was used in the definition of the SI unit of electric current—the Ampere—until 20 May 2019). To apply the equation, the point in space where the magnetic field is to be calculated is arbitrarily chosen ( r {\displaystyle \mathbf {r} } ).
The ampere is named for French physicist and mathematician André-Marie Ampère (1775–1836), who studied electromagnetism and laid the foundation of electrodynamics.In recognition of Ampère's contributions to the creation of modern electrical science, an international convention, signed at the 1881 International Exposition of Electricity, established the ampere as a standard unit of ...
The theory of special relativity plays an important role in the modern theory of classical electromagnetism.It gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another.
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 ...
Maxwell's equations on a plaque on his statue in Edinburgh. Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits.