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| {{about|magnetic materials|information about objects and devices that produce a magnetic field|magnet|fields that magnets and currents produce|magnetic field}}
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| [[File:Magnetic quadrupole moment.svg|thumb|240px|A magnetic quadrupole]]
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| {{electromagnetism|cTopic=[[Magnetostatics]]}}
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| '''Magnetism''' is a class of physical phenomena that includes forces exerted by [[magnet]]s on other magnets. It has its origin in electric currents and the fundamental [[magnetic moment]]s of elementary particles. These give rise to a [[magnetic field]] that acts on other currents and moments. All materials are influenced to some extent by a magnetic field. The strongest effect is on permanent magnets, which have persistent magnetic moments caused by [[ferromagnetism]]. Most materials do not have permanent moments. Some are attracted to a magnetic field ([[paramagnetism]]); others are repulsed by a magnetic field ([[diamagnetism]]); others have a much more complex relationship with an applied magnetic field ([[spin glass]] behavior and [[antiferromagnetism]]). Substances that are negligibly affected by magnetic fields are known as ''non-magnetic'' substances. They include [[copper]], [[aluminium]], [[gases]], and [[plastic]]. Pure [[oxygen]] exhibits magnetic properties when cooled to a [[liquids|liquid]] state.
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| The magnetic state (or phase) of a material depends on temperature (and other variables such as pressure and the applied magnetic field) so that a material may exhibit more than one form of magnetism depending on its temperature, etc.
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| == History ==
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| {{main|History of electromagnetism}}
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| [[Aristotle]] attributed the first of what could be called a scientific discussion on magnetism to [[Thales]] of [[Miletus]], who lived from about 625 BC to about 545 BC.<ref>{{cite web |url= http://galileoandeinstein.physics.virginia.edu/more_stuff/E&M_Hist.html|title= Historical Beginnings of Theories of Electricity and Magnetism|accessdate=2008-04-02 |last= Fowler|first= Michael|year= 1997}}</ref> Around the same time, in [[History of India|ancient India]], the [[Ayurveda|Indian surgeon]], [[Sushruta]], was the first to make use of the magnet for surgical purposes.<ref>{{Cite journal|title=Early Evolution of Power Engineering|first=Hugh P.|last=Vowles
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| |journal=[[Isis (journal)|Isis]]|volume=17|issue=2|year=1932|publisher=[[University of Chicago Press]]|pages=412–420 [419–20]|doi=10.1086/346662}}</ref> There is some evidence that the first use of magnetic materials for its properties predates this, J. B. Carlson suggests that the Olmec might have used hematite as a magnet earlier than 1000BC<ref>J B Carlson, "Lodestone Compass: Chinese or Olmec Primacy?", Science. 1975 Sep 5;189(4205):753-60</ref><ref>John B. Carlson, "Lodestone compass: Chinese or Olmec primacy?". ''Science,'' '''volume 189''', issue 4025, (pages 753-760) (1975)
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| http://www.bcin.ca/Interface/openbcin.cgi?submit=submit&Chinkey=55582</ref>
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| In [[History of China#Ancient China|ancient China]], the earliest literary reference to magnetism lies in a 4th-century BC book named after its author, ''The Master of Demon Valley'' (鬼谷子): "The [[lodestone]] makes iron come or it attracts it."<ref>Li Shu-hua, “Origine de la Boussole 11. Aimant et Boussole,” ''Isis'', Vol. 45, No. 2. (Jul., 1954), p.175</ref> The earliest mention of the attraction of a needle appears in a work composed between AD 20 and 100 (''Louen-heng''): "A lodestone attracts a needle."<ref>Li Shu-hua, “Origine de la Boussole 11. Aimant et Boussole,” ''Isis'', Vol. 45, No. 2. (Jul., 1954), p.176</ref> The [[History of science and technology in China|Chinese scientist]] [[Shen Kuo]] (1031–1095) was the first person to write of the magnetic needle compass and that it improved the accuracy of navigation by employing the [[astronomical]] concept of [[true north]] ''([[Dream Pool Essays]]'', AD 1088), and by the 12th century the Chinese were known to use the lodestone [[compass]] for navigation. They sculpted a directional spoon from lodestone in such a way that the handle of the spoon always pointed south.
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| [[Alexander Neckam]], by 1187, was the first in [[Europe]] to describe the compass and its use for navigation. In 1269, [[Peter of Maricourt|Peter Peregrinus de Maricourt]] wrote the ''Epistola de magnete'', the first extant treatise describing the properties of magnets. In 1282, the properties of magnets and the dry compass were discussed by Al-Ashraf, a [[Islamic physics|Yemeni physicist]], [[Islamic astronomy|astronomer]], and [[Islamic geography|geographer]].<ref>{{Cite journal|title=Two Early Arabic Sources On The Magnetic Compass|first=Petra G.|last=Schmidl|journal=Journal of Arabic and Islamic Studies|year=1996–1997|volume=1|pages=81–132}}</ref>
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| [[File:M Faraday Th Phillips oil 1842.jpg|thumb|upright=0.75|Michael Faraday, 1842]]
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| In 1600, [[William Gilbert (astronomer)|William Gilbert]] published his ''[[De Magnete|De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure]]'' (''On the Magnet and Magnetic Bodies, and on the Great Magnet the Earth''). In this work he describes many of his experiments with his model earth called the [[terrella]]. From his experiments, he concluded that the [[Earth's magnetic field|Earth]] was itself magnetic and that this was the reason compasses pointed north (previously, some believed that it was the pole star ([[Polaris]]) or a large magnetic island on the north pole that attracted the compass).
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| An understanding of the relationship between [[electricity]] and magnetism began in 1819 with work by [[Hans Christian Ørsted|Hans Christian Oersted]], a professor at the University of Copenhagen, who discovered more or less by accident that an electric current could influence a compass needle. This landmark experiment is known as Oersted's Experiment. Several other experiments followed, with [[André-Marie Ampère]], who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through the perimeter of the path; [[Carl Friedrich Gauss]]; [[Jean-Baptiste Biot]] and [[Félix Savart]], both of which in 1820 came up with the [[Biot-Savart Law]] giving an equation for the magnetic field from a current-carrying wire; [[Michael Faraday]], who in 1831 found that a time-varying magnetic flux through a loop of wire induced a voltage, and others finding further links between magnetism and electricity. [[James Clerk Maxwell]] synthesized and expanded these insights into [[Maxwell's equations]], unifying electricity, magnetism, and [[optics]] into the field of [[electromagnetism]]. In 1905, [[Einstein]] used these laws in motivating his theory of [[special relativity]],<ref name="Moving">[http://www.fourmilab.ch/etexts/einstein/specrel/www/ A. Einstein: "On the Electrodynamics of Moving Bodies"], June 30, 1905.</ref> requiring that the laws held true in all [[inertial reference frame]]s.
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| Electromagnetism has continued to develop into the 21st century, being incorporated into the more fundamental theories of [[gauge theory]], [[quantum electrodynamics]], [[electroweak theory]], and finally the [[standard model]].
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| == Sources of magnetism ==
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| {{see also|Magnetic moment}}
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| Magnetism, at its root, arises from two sources:
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| # [[Electric current]] (see ''[[electron magnetic dipole moment]]'').
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| # [[Nuclear magnetic moment]]s of atomic nuclei. These moments are typically thousands of times smaller than the electrons' magnetic moments, so they are negligible in the context of the magnetization of materials. Nuclear magnetic moments are very important in other contexts, particularly in [[nuclear magnetic resonance]] (NMR) and [[magnetic resonance imaging]] (MRI).
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| Ordinarily, the enormous number of electrons in a material are arranged such that their magnetic moments (both orbital and intrinsic) cancel out. This is due, to some extent, to electrons combining into pairs with opposite intrinsic magnetic moments as a result of the [[Pauli exclusion principle]] (see ''[[electron configuration]]''), or combining into filled [[electron subshell|subshells]] with zero net orbital motion. In both cases, the electron arrangement is so as to exactly cancel the magnetic moments from each electron. Moreover, even when the [[electron configuration]] ''is'' such that there are unpaired electrons and/or non-filled subshells, it is often the case that the various electrons in the solid will contribute magnetic moments that point in different, random directions, so that the material will not be magnetic.
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| However, sometimes — either spontaneously, or owing to an applied external magnetic field — each of the electron magnetic moments will be, on average, lined up. Then the material can produce a net total magnetic field, which can potentially be quite strong.
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| The magnetic behavior of a material depends on its structure, particularly its [[electron configuration]], for the reasons mentioned above, and also on the temperature. At high temperatures, random [[thermal motion]] makes it more difficult for the electrons to maintain alignment.
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| == Topics ==
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| [[File:Magnetism.svg|thumb|center|upright=2.7|Hierarchy of types of magnetism.<ref name=Meyers1>{{cite book |title=Introductory solid state physics |author=HP Meyers |url=http://books.google.com/?id=Uc1pCo5TrYUC&pg=PA322 |page=362; Figure 11.1 |isbn=0-7484-0660-3 |year=1997 |publisher=CRC Press |edition=2}}</ref>]]
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| === Diamagnetism ===
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| {{main|Diamagnetism}}
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| Diamagnetism appears in all materials, and is the tendency of a material to oppose an applied magnetic field, and therefore, to be repelled by a magnetic field. However, in a material with paramagnetic properties (that is, with a tendency to enhance an external magnetic field), the paramagnetic behavior dominates.<ref name=Westbrook>
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| {{cite book |title=MRI (Magnetic Resonance Imaging) in practice |author=Catherine Westbrook, Carolyn Kaut, Carolyn Kaut-Roth |isbn=0-632-04205-2 |url=http://books.google.com/?id=Qq1SHDtS2G8C&pg=PA217 |page=217 |edition=2|publisher=Wiley-Blackwell |year=1998}}
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| </ref> Thus, despite its universal occurrence, diamagnetic behavior is observed only in a purely diamagnetic material. In a diamagnetic material, there are no unpaired electrons, so the intrinsic electron magnetic moments cannot produce any bulk effect. In these cases, the magnetization arises from the electrons' orbital motions, which can be understood [[classical physics|classically]] as follows:
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| :When a material is put in a magnetic field, the electrons circling the nucleus will experience, in addition to their [[Coulomb's law|Coulomb]] attraction to the nucleus, a [[Lorentz force]] from the magnetic field. Depending on which direction the electron is orbiting, this force may increase the [[centripetal force]] on the electrons, pulling them in towards the nucleus, or it may decrease the force, pulling them away from the nucleus. This effect systematically increases the orbital magnetic moments that were aligned opposite the field, and decreases the ones aligned parallel to the field (in accordance with [[Lenz's law]]). This results in a small bulk magnetic moment, with an opposite direction to the applied field.
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| Note that this description is meant only as an [[heuristic]]; a proper understanding requires a [[quantum mechanics|quantum-mechanical]] description.
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| Note that all materials undergo this orbital response. However, in paramagnetic and ferromagnetic substances, the diamagnetic effect is overwhelmed by the much stronger effects caused by the unpaired electrons.
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| === Paramagnetism ===
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| {{main|Paramagnetism}}
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| In a paramagnetic material there are ''unpaired electrons'', i.e. [[atomic orbital|atomic]] or [[molecular orbital]]s with exactly one electron in them. While paired electrons are required by the [[Pauli exclusion principle]] to have their intrinsic ('spin') magnetic moments pointing in opposite directions, causing their magnetic fields to cancel out, an unpaired electron is free to align its magnetic moment in any direction. When an external magnetic field is applied, these magnetic moments will tend to align themselves in the same direction as the applied field, thus reinforcing it.
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| === Ferromagnetism ===
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| [[File:Ferromagneses penzermek 1.jpg|thumb|upright=0.9|A permanent magnet holding up several coins]]
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| {{main|Ferromagnetism}}
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| A ferromagnet, like a paramagnetic substance, has unpaired electrons. However, in ''addition'' to the electrons' intrinsic magnetic moment's tendency to be parallel to ''an applied field'', there is also in these materials a tendency for these magnetic moments to orient parallel to ''each other'' to maintain a lowered-energy state. Thus, even when the applied field is removed, the electrons in the material maintain a parallel orientation.
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| Every ferromagnetic substance has its own individual temperature, called the [[Curie temperature]], or Curie point, above which it loses its ferromagnetic properties. This is because the thermal tendency to disorder overwhelms the energy-lowering due to ferromagnetic order.
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| Some well-known ferromagnetic materials that exhibit easily detectable magnetic properties (to form [[magnet]]s) are [[nickel]], [[iron]], [[cobalt]], [[gadolinium]] and their [[alloy]]s.
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| ==== Magnetic domains ====
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| [[Image:Ferromag Matl Sketch.JPG|right|thumb|upright=0.7|Magnetic domains in ferromagnetic material.]]
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| {{main|Magnetic domains}}
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| The magnetic moment of atoms in a [[Ferromagnetism|ferromagnetic]] material cause them to behave something like tiny permanent magnets. They stick together and align themselves into small regions of more or less uniform alignment called [[magnetic domains]] or [[Weiss domains]]. Magnetic domains can be observed with a [[magnetic force microscope]] to reveal magnetic domain boundaries that resemble white lines in the sketch. There are many scientific experiments that can physically show magnetic fields.
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| [[Image:Ferromag Matl Magnetized.JPG|left|thumb|Effect of a magnet on the domains.]]When a domain contains too many molecules, it becomes unstable and divides into two domains aligned in opposite directions so that they stick together more stably as shown at the right.
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| When exposed to a magnetic field, the domain boundaries move so that the domains aligned with the magnetic field grow and dominate the structure as shown at the left. When the magnetizing field is removed, the domains may not return to an unmagnetized state. This results in the ferromagnetic material's being magnetized, forming a permanent magnet.
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| When magnetized strongly enough that the prevailing domain overruns all others to result in only one single domain, the material is [[Saturation (magnetic)|magnetically saturated]]. When a magnetized ferromagnetic material is heated to the [[Curie point]] temperature, the molecules are agitated to the point that the magnetic domains lose the organization and the magnetic properties they cause cease. When the material is cooled, this domain alignment structure spontaneously returns, in a manner roughly analogous to how a liquid can [[freezing|freeze]] into a crystalline solid.
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| === Antiferromagnetism ===
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| [[Image:Antiferromagnetic ordering.svg|thumb|Antiferromagnetic ordering]]
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| {{main|Antiferromagnetism}}
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| In an antiferromagnet, unlike a ferromagnet, there is a tendency for the intrinsic magnetic moments of neighboring valence electrons to point in ''opposite'' directions. When all atoms are arranged in a substance so that each neighbor is 'anti-aligned', the substance is '''antiferromagnetic'''. Antiferromagnets have a zero net magnetic moment, meaning no field is produced by them. Antiferromagnets are less common compared to the other types of behaviors, and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be seen to exhibit diamagnetic and ferrimagnetic properties.
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| In some materials, neighboring electrons want to point in opposite directions, but there is no geometrical arrangement in which ''each'' pair of neighbors is anti-aligned. This is called a [[spin glass]], and is an example of [[geometrical frustration]].
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| === Ferrimagnetism ===
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| [[Image:Ferrimagnetic ordering.svg|thumb|Ferrimagnetic ordering]]
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| {{main|Ferrimagnetism}}
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| Like ferromagnetism, '''ferrimagnets''' retain their magnetization in the absence of a field. However, like antiferromagnets, neighboring pairs of electron spins like to point in opposite directions. These two properties are not contradictory, because in the optimal geometrical arrangement, there is more magnetic moment from the sublattice of electrons that point in one direction, than from the sublattice that points in the opposite direction.
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| Most [[Ferrite (magnet)|ferrites]] are ferrimagnetic. The first discovered magnetic substance, [[magnetite]], is a ferrite and was originally believed to be a ferromagnet; [[Louis Néel]] disproved this, however, after discovering ferrimagnetism.
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| ===Superparamagnetism===
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| {{Main|Superparamagnetism}}
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| When a ferromagnet or ferrimagnet is sufficiently small, it acts like a single magnetic spin that is subject to [[Brownian motion]]. Its response to a magnetic field is qualitatively similar to the response of a paramagnet, but much larger.
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| ===Electromagnet===
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| An ''[[electromagnet]]'' is a type of [[magnet]] whose magnetism is produced by the flow of electric [[Current (electricity)|current]]. The magnetic field disappears when the current ceases.
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|
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| [[File:Electromagnet.gif|thumb|left|Electromagnets attracts paper clips when current is applied creating a magnetic field. The electromagnet loses them when current and magnetic field are removed.]]
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| ===Other types of magnetism===
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| * [[Molecular magnet]]
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| * [[Metamagnetism]]
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| * [[Molecule-based magnet]]
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| * [[Spin glass]]
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| == Magnetism, electricity, and special relativity ==
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| {{main|Classical electromagnetism and special relativity}}
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| As a consequence of Einstein's theory of special relativity, electricity and magnetism are fundamentally interlinked. Both magnetism lacking electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects as [[length contraction]], [[time dilation]], and the fact that the [[magnetic force]] is velocity-dependent. However, when both electricity and magnetism are taken into account, the resulting theory (electromagnetism) is fully consistent with special relativity.<ref name="Moving"/><ref>{{harvnb|Griffiths|1998|loc=chapter 12}}</ref> In particular, a phenomenon that appears purely electric to one observer may be purely magnetic to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity "mixes" electricity and magnetism into a single, inseparable phenomenon called electromagnetism, analogous to how relativity "mixes" space and time into [[spacetime]].
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| == Magnetic fields in a material ==
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| {{See also|Magnetic field#H and B inside and outside of magnetic materials}}
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| In a vacuum,
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| :<math>\mathbf{B} \ = \ \mu_0\mathbf{H}, </math>
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| where {{math|μ<sub>0</sub>}} is the [[vacuum permeability]].
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| In a material,
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| :<math>\mathbf{B} \ = \ \mu_0(\mathbf{H} + \mathbf{M}). \ </math>
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| The quantity {{math|μ<sub>0</sub>'''M'''}} is called ''magnetic polarization''. | |
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| If the field {{math|'''H'''}} is small, the response of the magnetization {{math|'''M'''}} in a [[diamagnet]] or [[paramagnet]] is approximately linear:
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| :<math> \mathbf{M} = \chi \mathbf{H},</math>
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| the constant of proportionality being called the magnetic susceptibility. If so,
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| :<math>\mu_0(\mathbf{H} + \mathbf{M}) \ = \ \mu_0(1+\chi) \mathbf{H} \ = \ \mu_r\mu_0 \mathbf{H} \ = \ \mu \mathbf{H}.</math>
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| In a hard magnet such as a ferromagnet, {{math|'''M'''}} is not proportional to the field and is generally nonzero even when {{math|'''H'''}} is zero (see [[Remanence]]).
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| == Magnetic force ==
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| [[Image:Magnet0873.png|thumb|Magnetic lines of force of a bar magnet shown by iron filings on paper]]
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| {{main|Magnetic field}}
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| The phenomenon of magnetism is "mediated" by the magnetic field. An electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.
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| Maxwell's equations, which simplify to the [[Biot-Savart law]] in the case of steady currents, describe the origin and behavior of the fields that govern these forces. Therefore magnetism is seen whenever electrically [[electric charge|charged particles]] are in [[Motion (physics)|motion]]---for example, from movement of electrons in an [[electric current]], or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" [[magnetic dipole]]s arising from quantum-mechanical [[Spin (physics)|spin]].
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| The same situations that create magnetic fields — charge moving in a current or in an atom, and intrinsic magnetic dipoles — are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole. | |
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| When a charged particle moves through a [[Magnetic field#B and H|magnetic field]] '''B''', it feels a [[Lorentz force]] '''F''' given by the [[cross product]]:<ref>{{Cite book |first = John David |last = Jackson |author-link=J. D. Jackson |title = Classical electrodynamics |edition = 3rd|location = New York, [NY.] |publisher = [[John Wiley & Sons|Wiley]] | year = 1999 |isbn = 0-471-30932-X |postscript = <!--None-->}}</ref>
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| : <math>\mathbf{F} = q (\mathbf{v} \times \mathbf{B})</math>
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| where
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| : <math>q</math> is the electric charge of the particle, and
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| : '''v''' is the [[velocity]] [[Vector (geometric)|vector]] of the particle
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| Because this is a cross product, the force is [[perpendicular]] to both the motion of the particle and the magnetic field. It follows that the magnetic force does no [[mechanical work|work]] on the particle; it may change the direction of the particle's movement, but it cannot cause it to speed up or slow down. The magnitude of the force is
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| : <math>F=qvB\sin\theta\,</math>
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| where <math>\theta</math> is the angle between '''v''' and '''B'''.
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| One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the [[index finger]] "V", the [[middle finger]] "B", and the [[thumb]] "F" with your right hand. When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also [[right hand rule]].
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| == Magnetic dipoles ==
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| {{main|Magnetic dipole}}
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| A very common source of magnetic field shown in nature is a [[dipole]], with a "[[South pole]]" and a "[[North pole]]", terms dating back to the use of magnets as compasses, interacting with the [[Earth's magnetic field]] to indicate North and South on the [[globe]]. Since opposite ends of magnets are attracted, the north pole of a magnet is attracted to the south pole of another magnet. The Earth's [[North Magnetic Pole]] (currently in the Arctic Ocean, north of Canada) is physically a south pole, as it attracts the north pole of a compass.
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| A magnetic field contains [[energy]], and physical systems move toward configurations with lower energy. When diamagnetic material is placed in a magnetic field, a ''magnetic dipole'' tends to align itself in opposed polarity to that field, thereby lowering the net field strength. When ferromagnetic material is placed within a magnetic field, the magnetic dipoles align to the applied field, thus expanding the domain walls of the magnetic domains.
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| === Magnetic monopoles ===
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| {{main|Magnetic monopole}}
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| Since a bar magnet gets its ferromagnetism from electrons distributed evenly throughout the bar, when a bar magnet is cut in half, each of the resulting pieces is a smaller bar magnet. Even though a magnet is said to have a north pole and a south pole, these two poles cannot be separated from each other. A monopole — if such a thing exists — would be a new and fundamentally different kind of magnetic object. It would act as an isolated north pole, not attached to a south pole, or vice versa. Monopoles would carry "magnetic charge" analogous to electric charge. Despite systematic searches since 1931, {{As of|2010|lc=on}}, they have never been observed, and could very well not exist.<ref>Milton mentions some inconclusive events (p.60) and still concludes that "no evidence at all of magnetic monopoles has survived" (p.3). {{cite journal |last=Milton |first=Kimball A. |title=Theoretical and experimental status of magnetic monopoles |journal=Reports on Progress in Physics |volume=69 |issue=6 |date=June 2006 |pages=1637–1711 |doi=10.1088/0034-4885/69/6/R02 |arxiv=hep-ex/0602040|bibcode = 2006RPPh...69.1637M }}.</ref>
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| Nevertheless, some [[theoretical physics]] models predict the existence of these [[magnetic monopoles]]. [[Paul Dirac]] observed in 1931 that, because electricity and magnetism show a certain [[symmetry]], just as [[Quantum electrodynamics|quantum theory]] predicts that individual [[positive charge|positive]] or [[negative charge|negative]] electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge---that is, why the observed [[elementary particles]] carry charges that are multiples of the charge of the electron.
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| Certain [[grand unified theories]] predict the existence of monopoles which, unlike elementary particles, are [[solitons]] (localized energy packets). The initial results of using these models to estimate the number of monopoles created in the [[big bang]] contradicted cosmological observations — the monopoles would have been so plentiful and massive that they would have long since halted the expansion of the universe. However, the idea of [[Cosmic inflation|inflation]] (for which this problem served as a partial motivation) was successful in solving this problem, creating models in which monopoles existed but were rare enough to be consistent with current observations.<ref>{{cite book |first=Alan|last=Guth|authorlink=Alan Guth|title=The Inflationary Universe: The Quest for a New Theory of Cosmic Origins|isbn=0-201-32840-2|publisher=Perseus|year=1997 |oclc=38941224}}.</ref>
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| == Quantum-mechanical origin of magnetism ==
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| In principle all kinds of magnetism originate (similar to [[Superconductivity]]) from specific quantum-mechanical phenomena (e.g. [[Mathematical formulation of quantum mechanics]], in particular the chapters on [[spin (physics)|spin]] and on the [[Pauli principle]]).
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| A successful model was developed already in 1927, by [[Walter Heitler]] and [[Fritz London]], who derived quantum-mechanically, how hydrogen molecules are formed from hydrogen atoms, i.e. from the atomic hydrogen orbitals <math> u_A</math> and <math>u_B</math> centered at the nuclei ''A'' and ''B'', see below. That this leads to magnetism, is not at all obvious, but will be explained in the following.
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| According the Heitler-London theory, so-called two-body molecular <math>\sigma</math>-orbitals are formed, namely the resulting orbital is:
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| :<math>\psi(\mathbf r_1,\,\,\mathbf r_2)=\frac{1}{\sqrt{2}}\,\,\left (u_A(\mathbf r_1)u_B(\mathbf r_2)+u_B(\mathbf r_1)u_A(\mathbf r_2)\right )</math>
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| Here the last product means that a first electron, '''r'''<sub>1</sub>, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus. This "exchange" phenomenon is an expression for the quantum-mechanical property that particles with identical properties cannot be distinguished. It is specific not only for the formation of [[chemical bond]]s, but as we will see, also for magnetism, i.e. in this connection the term [[exchange interaction]] arises, a term which is essential for the origin of magnetism, and which is stronger, roughly by factors 100 and even by 1000, than the energies arising from the electrodynamic dipole-dipole interaction.
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| As for the ''spin function'' <math>\chi (s_1,s_2)</math>, which is responsible for the magnetism, we have the already mentioned Pauli's principle, namely that a symmetric orbital (i.e. with the + sign as above) must be multiplied with an antisymmetric spin function (i.e. with a − sign), and ''vice versa''. Thus:
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| :<math>\chi (s_1,\,\,s_2)=\frac{1}{\sqrt{2}}\,\,\left (\alpha (s_1)\beta (s_2)-\beta (s_1)\alpha (s_2)\right )</math>,
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| I.e., not only <math>u_A</math> and <math>u_B</math> must be substituted by ''α'' and ''β'', respectively (the first entity means "spin up", the second one "spin down"), but also the sign + by the − sign, and finally '''r'''<sub>i</sub> by the discrete values ''s''<sub>i</sub> (= ±½); thereby we have <math>\alpha(+1/2)=\beta(-1/2)=1</math> and <math>\alpha(-1/2)=\beta(+1/2)=0</math>. The "[[singlet state]]", i.e. the − sign, means: the spins are ''antiparallel'', i.e. for the solid we have [[antiferromagnetism]], and for two-atomic molecules one has [[diamagnetism]]. The tendency to form a (homoeopolar) chemical bond (this means: the formation of a ''symmetric'' molecular orbital, i.e. with the + sign) results through the Pauli principle automatically in an ''antisymmetric'' spin state (i.e. with the − sign). In contrast, the Coulomb repulsion of the electrons, i.e. the tendency that they try to avoid each other by this repulsion, would lead to an ''antisymmetric'' orbital function (i.e. with the − sign) of these two particles, and complementary to a ''symmetric'' spin function (i.e. with the + sign, one of the so-called "[[triplet state|triplet functions]]"). Thus, now the spins would be ''parallel'' ([[ferromagnetism]] in a solid, [[paramagnetism]] in two-atomic gases).
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| The last-mentioned tendency dominates in the metals [[iron]], [[cobalt]] and [[nickel]], and in some rare earths, which are ''ferromagnetic''. Most of the other metals, where the first-mentioned tendency dominates, are ''nonmagnetic'' (e.g. [[sodium]], [[aluminium]], and [[magnesium]]) or ''antiferromagnetic'' (e.g. [[manganese]]). Diatomic gases are also almost exclusively diamagnetic, and not paramagnetic. However, the oxygen molecule, because of the involvement of π-orbitals, is an exception important for the life-sciences.
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| The Heitler-London considerations can be generalized to the [[Heisenberg model (classical)|Heisenberg model]] of magnetism (Heisenberg 1928).
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| The explanation of the phenomena is thus essentially based on all subtleties of quantum mechanics, whereas the electrodynamics covers mainly the phenomenology.
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| == Units of electromagnetism ==
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| ===SI units related to magnetism===
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| {|class="wikitable"
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| !colspan="5"|[[SI]] electromagnetism units
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| |-
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| !Symbol<ref>{{GreenBookRef2nd|pages=14–15}}</ref>
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| !Name of Quantity
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| !Derived Units
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| !Conversion of International to [[SI base unit]]s
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| |-
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| :''I''
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| |[[Electric current]]
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| |[[ampere]] ([[SI base unit]])
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| |<math>\mathrm{A=C\ s^{-1}}</math>
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| |-
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| :''q''
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| |[[Electric charge]]
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| |[[coulomb]]
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| |<math>\mathrm{C=A\ s}</math>
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| |-
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| |<math>U,\ \Delta V,\ \Delta\phi,\ \Epsilon</math>
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| |[[Potential difference]]; [[Electromotive force]]
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| |[[volt]]
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| |<math>\mathrm{V=J\ C^{-1}=kg\ A^{-1}m^2s^{-3}}</math>
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| |-
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| |<math>R;\ \Zeta;\ \Chi</math>
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| |[[Electric resistance]]; [[Electrical impedance|Impedance]]; [[Reactance (electronics)|Reactance]]
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| |[[Ohm (unit)|ohm]]
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| |<math>\mathrm{\Omega=V\ A^{-1}=kg\ m^{2} \ A^{-2}s^{-3}}</math>
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| |-
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| |<math>\ \rho</math>
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| |[[Resistivity]]
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| |[[Ohm (unit)|ohm]] [[metre]]
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| |<math>\mathrm{\Omega\ m=kg\ A^{-2}m^3s^{-3}}</math>
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| |-
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| |<math>\ \Rho</math>
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| |[[Electric power]]
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| |[[watt]]
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| |<math>\mathrm{W=V\ A=kg\ m^2s^{-3}}</math>
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| |-
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| |<math>\ C</math>
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| |[[Capacitance]]
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| |[[farad]]
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| |<math>\mathrm{F=C\ V^{-1}=A^2kg^{-1}m^{-2}s^4}</math>
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| |-
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| |<math>\mathbf{\Epsilon}</math>
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| |[[Electric field]] strength
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| |[[volt]] per [[metre]]
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| |<math>\mathrm{V\ m^{-1}=C^{-1}N=kg\ A^{-1}m\ s^{-3}}</math>
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| |-
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| |<math>\mathbf{D}</math>
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| |[[Electric displacement field]]
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| |[[Coulomb]] per [[square metre]]
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| |<math>\mathrm{C\ m^{-2}=A\ m^{-2}s}</math>
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| |-
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| |<math>\varepsilon</math>
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| |[[Permittivity]]
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| |[[farad]] per [[metre]]
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| |<math>\mathrm{F\ m^{-1}=A^{2}kg^{-1}m^{-3}s^{4}}</math>
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| |-
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| |<math>\!\chi_e</math>
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| |[[Electric susceptibility]]
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| |[[Dimensionless quantity|Dimensionless]]
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| |-
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| |<math>\Beta;\ G;\ \Upsilon</math>
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| |[[Electrical conductance|Conductance]]; [[Admittance]]; [[Susceptance]]
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| |[[Siemens (unit)|siemens]]
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| |<math>\ \mathrm{S=\Omega^{-1}=kg^{-1}A^2m^{-2}s^3}</math>
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| |-
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| |<math>\gamma,\ \kappa,\ \sigma</math>
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| |[[Electrical conductivity|Conductivity]]
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| |[[siemens (unit)|siemens]] per [[metre]]
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| |<math>\mathrm{S\ m^{-1}=A^2kg^{-1}m^{-3}s^3}</math>
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| |-
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| |<math>\ \mathbf{B}</math>
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| |[[Magnetic field|Magnetic flux density, Magnetic induction]]
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| |[[tesla (unit)|tesla]]
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| |<math>\mathrm{T=Wb\ m^{-2}=kg\ A^{-1}s^{-2}}</math>
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| |-
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| |<math>\ \Phi</math>
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| |[[Magnetic flux]]
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| |[[weber (unit)|weber]]
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| |<math>\mathrm{Wb=V\ s=kg\ A^{-1}m^2s^{-2}}</math>
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| |-
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| |<math>\mathbf{H}</math>
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| |[[Magnetic field]] strength
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| |[[ampere]] per [[metre]]
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| |<math>\mathrm{A\ m^{-1}}</math>
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| |-
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| |<math>L,\ \Mu</math>
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| |[[Inductance]]
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| |[[henry (unit)|henry]]
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| |<math>\mathrm{H=Wb\ A^{-1}=V\ A^{-1}s=kg\ A^{-2}m^2s^{-2}}</math>
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| |-
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| |<math>\ \mu</math>
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| |[[Permeability (electromagnetism)|Permeability]]
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| |[[henry (unit)|henry]] per [[metre]]
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| |<math>\mathrm{H m^{-1}=kg\ A^{-2}m\ s^{-2}}</math>
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| |-
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| |<math>\ \chi</math>
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| |[[Magnetic susceptibility]]
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| |[[Dimensionless quantity|Dimensionless]]
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| |}
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| === Other units ===
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| * [[gauss (unit)|gauss]] — The '''gauss''' is the [[centimeter-gram-second]] (CGS) [[units of measurement|unit]] of magnetic field (denoted '''B''').
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| * [[oersted]] — The '''oersted''' is the CGS unit of [[Magnetic field#B and H|magnetizing field]] (denoted '''H''').
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| * [[maxwell (unit)|maxwell]] — The '''maxwell''' is the CGS unit for [[magnetic flux]].
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| * gamma — is a unit of '''''magnetic flux density''''' that was commonly used before the [[tesla (unit)|tesla]] came into use (1.0 gamma = 1.0 nanotesla)
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| * ''μ''<sub>0</sub> — common symbol for the [[permeability (electromagnetism)|permeability]] of free space (4π×10<sup>−7</sup> [[newton (unit)|newton]]/([[ampere-turn]])<sup>2</sup>).
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| == Living things ==
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| Some [[organisms]] can detect magnetic fields, a phenomenon known as [[magnetoception]]. [[Magnetobiology]] studies magnetic fields as a [[medical]] treatment; fields naturally produced by an organism are known as [[biomagnetism]].
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| == See also ==
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| <div style="{{column-count|3}}">
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| * [[Coercivity]]
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| * [[Magnetar]]
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| * [[Magnetic bearing]]
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| * [[Magnetic circuit]]
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| * [[Magnetic cooling]]
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| * [[Magnetic field viewing film]]
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| * [[Magnetic stirrer]]
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| * [[Magnetic structure]]
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| * [[Micromagnetism]]
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| * [[Neodymium magnet]]
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| * [[Plastic magnet]]
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| * [[Rare-earth magnet]]
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| * [[Spin wave]]
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| * [[Spontaneous magnetization]]
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| * [[Vibrating sample magnetometer]]
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| * [[Gravitomagnetism]]
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| </div>
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| == References ==
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| {{Reflist}}
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| == Further reading ==
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| {{refbegin}}
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| * {{cite book | author=Furlani, Edward P. | title=Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications | publisher=Academic Press | year=2001 | isbn=0-12-269951-3 | oclc=162129430}}
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| * {{cite book | last1=Griffiths |first1=David J.|title=Introduction to Electrodynamics (3rd ed.)| publisher=Prentice Hall |year=1998 |isbn=0-13-805326-X | oclc=40251748|ref=harv}}
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| * {{cite book | author=Kronmüller, Helmut.|title=Handbook of Magnetism and Advanced Magnetic Materials, 5 Volume Set| publisher=John Wiley & Sons|year=2007 |isbn=978-0-470-02217-7 | oclc=124165851}}
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| * {{cite book | author=Tipler, Paul | title=Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.) | publisher=W. H. Freeman | year=2004 | isbn=0-7167-0810-8 | oclc=51095685}}
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| * {{cite book | author=David K. Cheng | title=Field and Wave Electromagnetics | publisher=Addison-Wesley Publishing Company, Inc. | year=1992 | isbn=0-201-12819-5 }}
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| {{refend}}
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| == External links ==
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| {{Wikibooks|School science}}
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| {{Wiktionary}}
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| * {{In Our Time|Magnetism|p003k9dd|Magnetism}}
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| * [http://www.exploratorium.edu/snacks/iconmagnetism.html The Exploratorium Science Snacks – Snacks about Magnetism]
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| * [http://www.lightandmatter.com/html_books/0sn/ch11/ch11.html Electromagnetism] - a chapter from an online textbook
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| * [http://www.youtube.com/watch?v=wMFPe-DwULM Video: The physicist Richard Feynman answers the question, Why do bar magnets attract or repel each other?]
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| * [http://www.antiquebooks.net/readpage.html#gilbert On the Magnet, 1600] First scientific book on magnetism by the father of electrical engineering. Full English text, full text search.
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| {{magnetic states}}
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| [[Category:Magnetism| ]]
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