Editing Magnetic field (section)

===Mathematical development===
[[File:Hans Christian Ørsted, Der Geist in der Natur, 1854.tiff|thumb|[[Hans Christian Ørsted]], ''Der Geist in der Natur'', 1854]]

In 1750, [[John Michell]] stated that magnetic poles attract and repel in accordance with an [[inverse square law]]<ref name=Whittaker1910 />{{rp|p=56}} [[Charles-Augustin de Coulomb]] experimentally verified this in 1785 and stated explicitly that north and south poles cannot be separated.<ref name=Whittaker1910 />{{rp|p=59}} Building on this force between poles, [[Siméon Denis Poisson]] (1781–1840) created the first successful model of the magnetic field, which he presented in 1824.<ref name=Whittaker1910 />{{rp|p=64}} In this model, a magnetic {{math|'''H'''}}-field is produced by ''magnetic poles'' and magnetism is due to small pairs of north–south magnetic poles.

Three discoveries in 1820 challenged this foundation of magnetism. [[Hans Christian Ørsted]] demonstrated that a current-carrying wire is surrounded by a circular magnetic field.{{refn|group="note"|During a lecture demonstration on the effects of a current on a campus needle, Ørsted showed that when a current-carrying wire is placed at a right angle with the compass, nothing happens. When he tried to orient the wire parallel to the compass needle, however, it produced a pronounced deflection of the compass needle. By placing the compass on different sides of the wire, he was able to determine the field forms perfect circles around the wire.<ref name=Whittaker1910 />{{rp|p=85}}}}<ref>{{cite encyclopedia|last1=Williams|first1=L. Pearce|date=1974|page=185| location=New York|title=Oersted, Hans Christian|url=https://archive.org/details/dictionaryofscie10gill/page/184|encyclopedia=Dictionary of Scientific Biography|editor-last1=Gillespie|editor-first1=C. C.|publisher=Charles Scribner's Sons}}</ref> Then [[André-Marie Ampère]] showed that parallel wires with currents attract one another if the currents are in the same direction and repel if they are in opposite directions.<ref name=Whittaker1910 />{{rp|p=87}}<ref>{{cite book|last1=Blundell|first1=Stephen J.|title=Magnetism: A Very Short Introduction|date=2012|publisher=OUP Oxford|isbn=9780191633720|page=31}}</ref> Finally, [[Jean-Baptiste Biot]] and [[Félix Savart]] announced empirical results about the forces that a current-carrying long, straight wire exerted on a small magnet, determining the forces were inversely proportional to the perpendicular distance from the wire to the magnet.<ref name=Tricker23>{{cite book|last1=Tricker|first1=R. A. R.|title=Early electrodynamics|url=https://archive.org/details/earlyelectrodyna0000tric|url-access=registration|date=1965|publisher=Pergamon|location=Oxford|page=[https://archive.org/details/earlyelectrodyna0000tric/page/23 23]}}</ref><ref name=Whittaker1910 />{{rp|p=86}} [[Laplace]] later deduced a law of force based on the differential action of a differential section of the wire,<ref name=Tricker23/><ref>{{cite journal| last1=Erlichson| first1=Herman|title=The experiments of Biot and Savart concerning the force exerted by a current on a magnetic needle| journal=American Journal of Physics|date=1998|volume=66|issue=5|page=389| doi=10.1119/1.18878| bibcode=1998AmJPh..66..385E |doi-access=free}}</ref> which became known as the [[Biot–Savart law]], as Laplace did not publish his findings.<ref>{{cite book|last1=Frankel| first1=Eugene|title=Jean-Baptiste Biot: The career of a physicist in nineteenth-century France|date=1972|publisher=Doctoral dissertation| location=Princeton University|page=334}}</ref>

Extending these experiments, Ampère published his own successful model of magnetism in 1825. In it, he showed the equivalence of electrical currents to magnets<ref name=Whittaker1910 />{{rp|p=88}} and proposed that magnetism is due to perpetually flowing loops of current instead of the dipoles of magnetic charge in Poisson's model.{{refn|group="note"|From the outside, the field of a dipole of magnetic charge has exactly the same form as a current loop when both are sufficiently small. Therefore, the two models differ only for magnetism inside magnetic material.}} Further, Ampère derived both [[Ampère's force law]] describing the force between two currents and [[Ampère's law]], which, like the Biot–Savart law, correctly described the magnetic field generated by a steady current. Also in this work, Ampère introduced the term [[electrodynamics]] to describe the relationship between electricity and magnetism.<ref name=Whittaker1910 />{{rp|pp=88–92}}

In 1831, [[Michael Faraday]] discovered [[electromagnetic induction]] when he found that a changing magnetic field generates an encircling electric field, formulating what is now known as [[Faraday's law of induction]].<ref name=Whittaker1910 />{{rp|pp=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.<ref name=Whittaker1910 />{{rp|p=222}} In the process, he introduced the magnetic vector potential, which was later shown to be equivalent to the underlying mechanism proposed by Faraday.<ref name=Whittaker1910 />{{rp|p=225}}

In 1850, [[Lord Kelvin]], then known as William Thomson, distinguished between two magnetic fields now denoted {{math|'''H'''}} and {{math|'''B'''}}. The former applied to Poisson's model and the latter to Ampère's model and induction.<ref name=Whittaker1910 />{{rp|p=224}} Further, he derived how {{math|'''H'''}} and {{math|'''B'''}} relate to each other and coined the term ''permeability''.<ref name=Whittaker1910 />{{rp|p=245}}<ref>[http://www.physik.uni-augsburg.de/lehrstuehle/did/Physik/Schulservice/Physikerkalender/06_26_Lord-Kelvin-of-Largs.pdf Lord Kelvin of Largs]. physik.uni-augsburg.de. 26 June 1824</ref>

Between 1861 and 1865, [[James Clerk Maxwell]] developed and published [[Maxwell's equations]], which explained and united all of [[classical theory|classical]] electricity and magnetism. The first set of these equations was published in a paper entitled ''[[:CCommons:File:On Physical Lines of Force.pdf|On Physical Lines of Force]]'' in 1861. These equations were valid but incomplete. Maxwell completed his set of equations in his later 1865 paper ''[[A Dynamical Theory of the Electromagnetic Field]]'' and demonstrated the fact that light is an [[electromagnetic wave]]. [[Heinrich Hertz]] published papers in 1887 and 1888 experimentally confirming this fact.<ref name=h202>Huurdeman, Anton A. (2003) ''The Worldwide History of Telecommunications''. Wiley. {{ISBN|0471205052}}. p. 202</ref><ref>{{cite web|url=http://www.hhi.fraunhofer.de/fraunhofer-hhi-the-institute/about-us/history-of-hhi/the-most-important-experiments.html|publisher=Fraunhofer Heinrich Hertz Institute|title=The most important Experiments – The most important Experiments and their Publication between 1886 and 1889|access-date=19 February 2016}}</ref>