In physics, **Ampère's law** is the magnetic equivalent of Gauss's law, discovered by André-Marie Ampère. It relates the circulating magnetic field in a closed loop to the electric current passing through the loop: In physics, Gausss law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. ...
André-Marie Ampère (January 20, 1775 – June 10, 1836), was a French physicist who is generally credited as one of the main discoverers of electromagnetism. ...
In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. ...
In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ...
where is the magnetic field, In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. ...
is an infinitesimal element (differential) of the closed loop *S*, In mathematics, an infinitesimal, or infinitely small number, is a number that is greater in absolute value than zero yet smaller than any positive real number. ...
A differential can mean one of several things: Differential (mathematics) Differential (mechanics) Differential signaling is used to carry high speed digital signals. ...
*I*_{enc} is the current enclosed by the curve *S*, μ_{0} is the permeability of free space, This article is in need of attention. ...
is the path integral along the closed loop *S*. This article is about path integrals in the general mathematical sense, and not the path integral formulation of physics which was studied by Richard Feynman. ...
## Generalized Ampère's law
James Clerk Maxwell noticed a logical inconsistency when applying Ampère's law on charging capacitors, and thus concluded that this law had to be incomplete. To resolve the problem, he came up with the concept of displacement current and made a generalized version of Ampère's law which was incorporated into Maxwell's equations. The generalized formula is as follows: James Clerk Maxwell James Clerk Maxwell (June 13, 1831 - November 5, 1879) was a Scottish physicist, born in Edinburgh. ...
Various types of capacitors A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. ...
Displacement current is a pseudocurrent invented in 1865 by James Clerk Maxwell when formulating what are today known as Maxwells equations. ...
Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...
where is the flux of electric field through the surface. This article is in need of attention. ...
In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ...
This *Ampère-Maxwell law* can also be stated in differential form: where the second term arises from the displacement current; omitting it yields the differential form of the original Ampère's law.
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