What Does Ampère’s Law Consists On?

Ampere´s Law consists of the “The magnetic field in space around an electric current is proportional to the electric current which serves as its source, just as the electric field in space is proportional to the charge which serves as its source. Ampere’s Law states that for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.”  http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html

“Hans Christian Oersted had just discovered the connection between electricity and magnetism. Meanwhile, a French physicist named André-Marie Ampère was experimenting with some wires, trying to learn more about the connection between current and the magnetic fields they create. Ampère would discover one of the most fundamental laws of electromagnetism: what we now call Ampère’s Law.

“In classical electromagnetism, Ampère’s circuital law (not to be confused with Ampère’s force law that André-Marie Ampèrediscovered in 1823) relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell (not Ampère) derived it using hydrodynamics in his 1861 paper “On Physical Lines of Force” and it is now one of the Maxwell equations, which form the basis of classical electromagnetism.

The original form of Maxwell’s circuital law, which he derived in his 1855 paper “On Faraday’s Lines of Force” based on an analogy to hydrodynamics, relates magnetic fields to electric currents that produce them. It determines the magnetic field associated with a given current or the current associated with a given magnetic field.

The original circuital law is only a correct law of physics in a magnetostatic situation, where the system is static except possibly for continuous steady currents within closed loops. For systems with electric fields that change over time, the original law (as given in this section) must be modified to include a term known as Maxwell’s correction ” https://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law

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