View source for Electromagnetism

{{Short description|Fundamental interaction between charged particles}}
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{{Redirect|Electromagnetics|the academic journal|Electromagnetics (journal){{!}}''Electromagnetics'' (journal)}}
{{Redirect|Electromagnetic force|the force exerted on particles by electromagnetic fields|Lorentz force}}
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[[File:Plasma globe 60th.jpg|thumb|300x300px|Electromagnetic interactions are responsible for the glowing filaments in this [[plasma globe]].]]
{{Electromagnetism|cTopic=-}}

In physics, '''electromagnetism''' is an interaction that occurs between [[particles]] with [[electric charge]] via [[electromagnetic fields]]. The electromagnetic force is one of the four [[fundamental forces]] of nature.<ref name="Rehm-2021">{{Cite web |last=Biggs |first=Ben |last2=Rehm |first2=Jeremy  |date=2021-12-23 |title=The four fundamental forces of nature |url=https://www.space.com/four-fundamental-forces.html |access-date=2025-08-15 |website=Space |language=en}}</ref> It is the dominant force in the interactions of [[atoms]] and [[molecules]]. Electromagnetism can be thought of as a combination of [[electrostatics]] and [[magnetism]], which are distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles. Electric forces cause an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs between charged particles in relative motion. These two forces are described in terms of electromagnetic fields. Macroscopic charged objects are described in terms of [[Coulomb's law]] for electricity and [[Ampère's force law]] for magnetism; the [[Lorentz force]] describes microscopic charged particles.

The electromagnetic force is responsible for many of the [[chemistry|chemical]] and physical phenomena observed in daily life. The electrostatic attraction between [[atomic nuclei]] and their [[electron]]s holds atoms together. Electric forces also allow different atoms to combine into molecules, including the [[macromolecule]]s such as [[proteins]] that form the basis of [[life]]. Meanwhile, magnetic interactions between the [[Electron magnetic moment|spin]] and [[Azimuthal quantum number|angular momentum]] magnetic moments of electrons also play a role in chemical reactivity; such relationships are studied in [[spin chemistry]]. Electromagnetism also plays several crucial roles in modern [[technology]]: electrical energy production, transformation and distribution; light, heat, and sound production and detection; fiber optic and wireless communication; sensors; computation; electrolysis; electroplating; and mechanical motors and actuators.

Electromagnetism has been studied since ancient times. Many ancient civilizations, including the [[Ancient Greece|Greeks]] and the [[Maya civilization|Mayans]], created wide-ranging theories to explain [[lightning]], [[static electricity]], and the attraction between magnetized pieces of [[iron ore]]. However, it was not until the late 18th century that scientists began to develop a mathematical basis for understanding the nature of electromagnetic interactions. In the 18th and 19th centuries, prominent scientists and mathematicians such as [[Charles-Augustin de Coulomb|Coulomb]], [[Gauss]] and [[Faraday]] developed namesake laws which helped to explain the formation and interaction of electromagnetic fields. This process culminated in the 1860s with the discovery of [[Maxwell's equations]], a set of four [[partial differential equation]]s which provide a complete description of classical electromagnetic fields. Maxwell's equations provided a sound mathematical basis for the relationships between electricity and magnetism that scientists had been exploring for centuries, and predicted the existence of self-sustaining [[electromagnetic waves]]. Maxwell postulated that such waves make up [[visible light]], which was later shown to be true. Gamma-rays, x-rays, ultraviolet, visible, infrared radiation, microwaves and radio waves were all determined to be electromagnetic radiation differing only in their range of frequencies.

In the modern era, scientists continue to refine the theory of electromagnetism to account for the effects of [[modern physics]], including [[quantum mechanics]] and [[Theory of relativity|relativity]]. The theoretical implications of electromagnetism, particularly the requirement that observations remain consistent when viewed from various moving frames of reference ([[relativistic electromagnetism]]) and the establishment of the speed of light based on properties of the medium of propagation ([[permeability (electromagnetism)|permeability]] and [[permittivity]]), helped inspire [[Albert Einstein|Einstein's]] theory of [[special relativity]] in 1905. [[Quantum electrodynamics]] (QED) modifies Maxwell's equations to be consistent with the [[quantization (physics)|quantized]] nature of matter. In QED, changes in the electromagnetic field are expressed in terms of discrete excitations, particles known as [[photons]], the [[quantum|quanta]] of light.

==History==
{{Main|History of electromagnetic theory}}

===Ancient world===
Investigation into electromagnetic phenomena began about 5,000 years ago. There is evidence that the ancient [[History of China|Chinese]],<ref>{{Cite book |last=Meyer |first=Herbert |title=A History of Electricity and Magnetism |year=1972 |page=2 |language=en}}</ref> [[Mayan civilization|Mayan]],<ref>{{Cite web |last=Learn |first=Joshua Rapp |title=Mesoamerican Sculptures Reveal Early Knowledge of Magnetism |url=https://www.smithsonianmag.com/science-nature/mesoamerican-sculptures-reveal-early-knowledge-magnetism-180972820/ |access-date=2022-12-07 |website=Smithsonian Magazine |language=en |archive-date=2022-12-07 |archive-url=https://web.archive.org/web/20221207191246/https://www.smithsonianmag.com/science-nature/mesoamerican-sculptures-reveal-early-knowledge-magnetism-180972820/ |url-status=live }} Summary of paper by Fu et al.</ref><ref name="Fu-2019">{{Cite journal |last1=Fu |first1=Roger R. |last2=Kirschvink |first2=Joseph L. |last3=Carter |first3=Nicholas |last4=Mazariegos |first4=Oswaldo Chinchilla |last5=Chigna |first5=Gustavo |last6=Gupta |first6=Garima |last7=Grappone |first7=Michael |date=2019-06-01 |title=Knowledge of magnetism in ancient Mesoamerica: Precision measurements of the potbelly sculptures from Monte Alto, Guatemala |url=https://www.sciencedirect.com/science/article/pii/S0305440318305776 |journal=Journal of Archaeological Science |volume=106 |pages=29–36 |doi=10.1016/j.jas.2019.03.001 |bibcode=2019JArSc.106...29F |issn=0305-4403}}</ref> and potentially even [[Ancient Egypt|Egyptian]] civilizations knew that the naturally magnetic mineral [[magnetite]] had attractive properties, and many incorporated it into their art and architecture.<ref>{{Citation |last1=du Trémolet de Lacheisserie |first1=É. |title=Magnetism, from the Dawn of Civilization to Today |date=2002 |url=https://doi.org/10.1007/978-0-387-23062-7_1 |work=Magnetism |pages=3–18 |editor-last=du Trémolet de Lacheisserie |editor-first=É. |place=New York, NY |publisher=Springer |language=en |doi=10.1007/978-0-387-23062-7_1 |isbn=978-0-387-23062-7 |access-date=2022-12-07 |last2=Gignoux |first2=D. |last3=Schlenker |first3=M. |editor2-last=Gignoux |editor2-first=D. |editor3-last=Schlenker |editor3-first=M. |archive-date=2024-10-03 |archive-url=https://web.archive.org/web/20241003193840/https://link.springer.com/referenceworkentry/10.1007/978-0-387-23062-7_1 |url-status=live }}</ref> Ancient people were also aware of [[lightning]] and [[static electricity]], although they had no idea of the mechanisms behind these phenomena. The [[Ancient Greece|Greek]] philosopher [[Thales of Miletus]] discovered around 600 B.C.E. that [[amber]] could acquire an electric charge when it was rubbed with cloth, which allowed it to pick up light objects such as pieces of straw. Thales also experimented with the ability of magnetic rocks to attract one other, and hypothesized that this phenomenon might be connected to the attractive power of amber, foreshadowing the deep connections between electricity and magnetism that would be discovered over 2,000 years later. Despite all this investigation, ancient civilizations had no understanding of the mathematical basis of electromagnetism, and often analyzed its impacts through the lens of [[religion]] rather than science (lightning, for instance, was considered to be a creation of the gods in many cultures).<ref>{{Cite book |last=Meyer |first=Herbert |title=A History of Electricity and Magnetism |year=1972 |pages=3–4 |language=en}}</ref>

===19th century===
[[File:A Treatise on Electricity and Magnetism Volume 2 003.jpg|thumb|Cover of ''A Treatise on Electricity and Magnetism'']]
Electricity and magnetism were originally considered to be two separate forces. This view changed with the publication of [[James Clerk Maxwell]]'s 1873 ''[[A Treatise on Electricity and Magnetism]]''<ref>{{Cite journal|date=24 April 1873|title=A Treatise on Electricity and Magnetism|url=https://www.nature.com/articles/007478a0|journal=Nature|language=en|volume=7|issue=182|pages=478–480|doi=10.1038/007478a0|bibcode=1873Natur...7..478.|s2cid=10178476|issn=0028-0836|access-date=8 February 2022|archive-date=23 October 2021|archive-url=https://web.archive.org/web/20211023150511/https://www.nature.com/articles/007478a0|url-status=live}}</ref> in which the interactions of positive and negative charges were shown to be mediated by one force. There are four main effects resulting from these interactions, all of which have been clearly demonstrated by experiments:
# Electric charges ''{{vanchor|attract}}'' or ''{{vanchor|repel}}'' one another with a force [[inversely proportional]] to the square of the distance between them: opposite charges attract, like charges repel.<ref>{{Cite web |date=2019-02-06 |title=Why Do Like Charges Repel And Opposite Charges Attract? |url=https://www.scienceabc.com/eyeopeners/like-charges-repel-opposite-charges-attract.html |access-date=2022-08-22 |website=Science ABC |language=en-US |archive-date=2022-08-22 |archive-url=https://web.archive.org/web/20220822120352/https://www.scienceabc.com/eyeopeners/like-charges-repel-opposite-charges-attract.html |url-status=live }}</ref>
# Magnetic poles (or states of polarization at individual points) attract or repel one another in a manner similar to positive and negative charges and always exist as pairs: every north pole is yoked to a south pole.<ref>{{Cite web |title=What Makes Magnets Repel? |url=https://sciencing.com/magnets-repel-7754550.html |access-date=2022-08-22 |website=Sciencing |date=27 December 2020 |language=en |archive-date=2022-09-26 |archive-url=https://web.archive.org/web/20220926214826/https://sciencing.com/magnets-repel-7754550.html |url-status=live }}</ref>
# An electric current inside a wire creates a corresponding circumferential magnetic field outside the wire. Its direction (clockwise or counter-clockwise) depends on the direction of the current in the wire.<ref name=lscience >{{Cite web |author1=Jim Lucas Contributions from Ashley Hamer |date=2022-02-18 |title=What Is Faraday's Law of Induction? |url=https://www.livescience.com/53509-faradays-law-induction.html |access-date=2022-08-22 |website=livescience.com |language=en |archive-date=2022-08-22 |archive-url=https://web.archive.org/web/20220822120351/https://www.livescience.com/53509-faradays-law-induction.html |url-status=live }}</ref>
# A current is induced in a loop of wire when it is moved toward or away from a magnetic field, or a magnet is moved towards or away from it; the direction of current depends on that of the movement.<ref name=lscience />
In April 1820, [[Hans Christian Ørsted]] observed that an electrical current in a wire caused a nearby compass needle to move. At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework. However, three months later he began more intensive investigations.<ref>{{Cite journal|date=1884-02-23|title=History of the Electric Telegraph|url=http://dx.doi.org/10.1038/scientificamerican02231884-6784supp|journal=Scientific American|volume=17|issue=425supp|pages=6784–6786|doi=10.1038/scientificamerican02231884-6784supp|issn=0036-8733|access-date=2022-02-08|archive-date=2024-10-03|archive-url=https://web.archive.org/web/20241003193822/https://www.scientificamerican.com/article/history-of-the-electric-telegraph1/|url-status=live}}</ref><ref>{{Cite book|title=Volta and the history of electricity|date=2003|publisher=U. Hoepli|editor-first1=Fabio|editor-last1=Bevilacqua|editor-first2=Enrico A.|editor-last2=Giannetto|isbn=88-203-3284-1|location=Milano|oclc=1261807533}}</ref> Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire. The [[CGS]] unit of [[Electromagnetic induction|magnetic induction]] ([[oersted]]) is named in honor of his contributions to the field of electromagnetism.<ref>{{Cite book|last=Roche|first=John J.|title=The mathematics of measurement : a critical history|date=1998|publisher=Athlone Press|isbn=0-485-11473-9|location=London|oclc=40499222}}</ref>

His findings resulted in intensive research throughout the scientific community in electrodynamics. They influenced French physicist [[André-Marie Ampère]]'s developments of a single mathematical form to represent the magnetic forces between current-carrying conductors. Ørsted's discovery also represented a major step toward a unified concept of energy.

This unification, which was observed by [[Michael Faraday]], extended by [[James Clerk Maxwell]], and partially reformulated by [[Oliver Heaviside]] and [[Heinrich Hertz]], is one of the key accomplishments of 19th-century [[mathematical physics]].<ref>{{cite book |last1=Darrigol |first1=Olivier |title=Electrodynamics from Ampère to Einstein |date=2000 |publisher=Oxford University Press |location=New York |isbn=0198505949 |url-access=registration |url=https://archive.org/details/electrodynamicsf0000darr }}</ref> It has had far-reaching consequences, one of which was the understanding of the nature of [[light]]. Unlike what was proposed by the electromagnetic theory of that time, light and other [[electromagnetic waves]] are at present seen as taking the form of [[quantum|quantized]], self-propagating [[oscillatory]] electromagnetic field disturbances called [[photon]]s. Different [[frequencies]] of oscillation give rise to the different forms of [[electromagnetic radiation]], from [[radio wave]]s at the lowest frequencies, to visible light at intermediate frequencies, to [[gamma ray]]s at the highest frequencies.

Ørsted was not the only person to examine the relationship between electricity and magnetism. In 1802, [[Gian Domenico Romagnosi]], an Italian legal scholar, deflected a magnetic needle using a Voltaic pile. The factual setup of the experiment is not completely clear, nor if current flowed across the needle or not. An account of the discovery was published in 1802 in an Italian newspaper, but it was largely overlooked by the contemporary scientific community, because Romagnosi seemingly did not belong to this community.<ref>{{cite book|last1=Martins |first1=Roberto de Andrade |title=Nuova Voltiana: Studies on Volta and his Times |chapter=Romagnosi and Volta's Pile: Early Difficulties in the Interpretation of Voltaic Electricity |volume=3 |editor=Fabio Bevilacqua |editor2=Lucio Fregonese |publisher=Università degli Studi di Pavia |pages=81–102 |chapter-url=http://ppp.unipv.it/collana/pages/libri/saggi/nuova%20voltiana3_pdf/cap4/4.pdf |access-date=2010-12-02 |url-status=dead |archive-url=https://web.archive.org/web/20130530200951/http://ppp.unipv.it/Collana/Pages/Libri/Saggi/Nuova%20Voltiana3_PDF/cap4/4.pdf |archive-date=2013-05-30 }}</ref>

An earlier (1735), and often neglected, connection between electricity and magnetism was reported by a Dr. Cookson.<ref>VIII. An account of an extraordinary effect of lightning in communicating magnetism. Communicated by Pierce Dod, M.D. F.R.S. from Dr. Cookson of Wakefield in Yorkshire.
Phil. Trans. 1735 39, 74-75, published 1 January 1735</ref> The account stated:<blockquote>A tradesman at Wakefield in Yorkshire, having put up a great number of knives and forks in a large box ...  and having placed the box in the corner of a large room, there happened a sudden storm of thunder, lightning, &c.  ... The owner emptying the box on a counter where some nails lay, the persons who took up the knives, that lay on the nails, observed that the knives took up the nails. On this the whole number was tried, and found to do the same, and that, to such a degree as to take up large nails, packing needles, and other iron things of considerable weight ...</blockquote> [[E. T. Whittaker]] suggested in 1910 that this particular event was responsible for lightning to be "credited with the power of magnetizing steel; and it was doubtless this which led Franklin in 1751 to attempt to magnetize a sewing-needle by means of the discharge of Leyden jars."<ref>[[E. T. Whittaker|Whittaker, E.T.]] (1910). [[A History of the Theories of Aether and Electricity|A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century]]. Longmans, Green and Company.</ref>

== A fundamental force ==
[[File:Circular.Polarization.Circularly.Polarized.Light Right.Handed.Animation.305x190.255Colors.gif|thumb|right|220px|Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation]]
The electromagnetic force is the second strongest of the four known [[fundamental forces]] and has unlimited range.<ref name="Rehm-2021" />
All other forces, known as [[Force#Non-fundamental forces|non-fundamental forces]].<ref>Browne, "Physics for Engineering and Science", p. 160: "Gravity is one of the fundamental forces of nature. The other forces such as friction, tension, and the normal force are derived from the electric force, another of the fundamental forces. Gravity is a rather weak force... The electric force between two protons is much stronger than the gravitational force between them."</ref> (e.g., [[friction]], contact forces) are derived from the four fundamental forces. At high energy, the [[weak force]] and electromagnetic force are unified as a single interaction called the [[electroweak interaction]].<ref>{{Cite journal |last1=Salam |first1=A. |last2=Ward |first2=J.C. |date=November 1964 |title=Electromagnetic and weak interactions |url=https://linkinghub.elsevier.com/retrieve/pii/0031916364907115 |journal=Physics Letters |language=en |volume=13 |issue=2 |pages=168–171 |doi=10.1016/0031-9163(64)90711-5 |bibcode=1964PhL....13..168S |access-date=2024-02-02 |archive-date=2024-04-16 |archive-url=https://web.archive.org/web/20240416150859/https://linkinghub.elsevier.com/retrieve/pii/0031916364907115 |url-status=live }}</ref>

Most of the forces involved in interactions between [[atom]]s are explained by electromagnetic forces between electrically charged [[atomic nuclei]] and [[electron]]s. The electromagnetic force is also involved in all forms of [[chemistry|chemical phenomena]].

Electromagnetism explains how materials carry momentum despite being composed of individual particles and empty space. The forces we experience when "pushing" or "pulling" ordinary material objects result from [[intermolecular force]]s between individual [[molecule]]s in our bodies and in the objects.

The effective forces generated by the momentum of electrons' movement is a necessary part of understanding atomic and intermolecular interactions. As electrons move between interacting atoms, they carry momentum with them. As a collection of electrons becomes more confined, their minimum momentum necessarily increases due to the [[Pauli exclusion principle]]. The behavior of matter at the molecular scale, including its density, is determined by the balance between the electromagnetic force and the force generated by the exchange of momentum carried by the electrons themselves.<ref>Purcell, "Electricity and Magnetism, 3rd Edition", p. 546: Ch 11 Section 6, "Electron Spin and Magnetic Moment."</ref>

==Classical electrodynamics==
{{Main|Classical electrodynamics}}

In 1600, [[William Gilbert (astronomer)|William Gilbert]] proposed, in his ''[[De Magnete]]'', that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects.<ref>{{Cite journal |last1=Malin |first1=Stuart |last2=Barraclough |first2=David |date=2000 |title=Gilbert's De Magnete: An early study of magnetism and electricity |url=http://doi.wiley.com/10.1029/00EO00163 |journal=Eos, Transactions American Geophysical Union |language=en |volume=81 |issue=21 |pages=233 |doi=10.1029/00EO00163 |bibcode=2000EOSTr..81..233M |issn=0096-3941 |access-date=2022-08-22 |archive-date=2024-10-03 |archive-url=https://web.archive.org/web/20241003193745/https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/00EO00163 |url-status=live }}</ref> Mariners had noticed that lightning strikes had the ability to disturb a compass needle. The link between lightning and electricity was not confirmed until [[Benjamin Franklin]]'s proposed experiments in 1752 were conducted on 10{{nbsp}}May 1752 by [[Thomas-François Dalibard]] of France using a {{convert|40|ft|m|adj=mid|-tall}} iron rod instead of a kite and he successfully extracted electrical sparks from a cloud.<ref>{{Cite web|url=http://www.mos.org/sln/toe/kite.html|title=Lightning! &#124; Museum of Science, Boston|access-date=2022-08-22|archive-date=2010-02-09|archive-url=https://web.archive.org/web/20100209131349/http://www.mos.org/sln/toe/kite.html|url-status=dead}}</ref><ref>{{Cite book |last=Tucker |first=Tom |title=Bolt of fate : Benjamin Franklin and his electric kite hoax |date=2003 |publisher=PublicAffairs |isbn=1-891620-70-3 |edition=1st |location=New York |oclc=51763922 }}</ref>

One of the first to discover and publish a link between human-made electric current and magnetism was [[Romagnosi|Gian Romagnosi]], who in 1802 noticed that connecting a wire across a [[voltaic pile]] deflected a nearby [[compass]] needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment.<ref name="Stern-2001">{{cite web |url=http://www-istp.gsfc.nasa.gov/Education/whmfield.html |title=Magnetic Fields – History |access-date=2009-11-27 |last1=Stern |first1=Dr. David P. |first2=Mauricio |last2=Peredo |date=2001-11-25 |publisher=NASA Goddard Space Flight Center |archive-date=2015-11-16 |archive-url=https://web.archive.org/web/20151116034519/http://www-istp.gsfc.nasa.gov/Education/whmfield.html |url-status=live }}</ref> Ørsted's work influenced Ampère to conduct further experiments, which eventually gave rise to a new area of physics: electrodynamics. By determining a force law for the interaction between elements of electric current, Ampère placed the subject on a solid mathematical foundation.<ref>{{Cite web |date=2016-01-13 |title=Andre-Marie Ampère |url=https://ethw.org/Andre-Marie_Amp%C3%A8re |access-date=2022-08-22 |website=ETHW |language=en |archive-date=2022-08-22 |archive-url=https://web.archive.org/web/20220822112621/https://ethw.org/Andre-Marie_Amp%C3%A8re |url-status=live }}</ref>

A theory of electromagnetism, known as [[classical electromagnetism]], was developed by several physicists during the period between 1820 and 1873, when [[James Clerk Maxwell]]'s [[A Treatise on Electricity and Magnetism|treatise]] was published, which unified previous developments into a single theory, proposing that light was an electromagnetic wave propagating in the ''luminiferous ether''.<ref>Purcell, p. 436. Chapter 9.3, "Maxwell's description of the electromagnetic field was essentially complete."</ref> In classical electromagnetism, the behavior of the electromagnetic field is described by a set of equations known as [[Maxwell's equations]], and the electromagnetic force is given by the [[Lorentz force law]].<ref>Purcell: p. 278: Chapter 6.1, "Definition of the Magnetic Field." Lorentz force and force equation.</ref>

One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with [[classical mechanics]], but it is compatible with special relativity. According to Maxwell's equations, the [[speed of light]] in vacuum is a universal constant that is dependent only on the [[electrical permittivity]] and [[magnetic permeability]] of [[free space]]. This violates [[Galilean invariance]], a long-standing cornerstone of classical mechanics. One way to reconcile the two theories (electromagnetism and classical mechanics) is to assume the existence of a [[luminiferous aether]] through which the light propagates. However, subsequent experimental efforts failed to detect the presence of the aether. After important contributions of [[Hendrik Lorentz]] and [[Henri Poincaré]], in 1905, [[Albert Einstein]] solved the problem with the introduction of special relativity, which replaced classical kinematics with a new theory of kinematics compatible with classical electromagnetism. (For more information, see [[History of special relativity]].)

In addition, relativity theory implies that in moving frames of reference, a magnetic field transforms to a field with a nonzero electric component and conversely, a moving electric field transforms to a nonzero magnetic component, thus firmly showing that the phenomena are two sides of the same coin. Hence the term "electromagnetism". (For more information, see [[Classical electromagnetism and special relativity]] and [[Covariant formulation of classical electromagnetism]].)

Today few problems in electromagnetism remain unsolved. These include: the lack of [[magnetic monopoles]], [[Abraham–Minkowski controversy]], the location in space of the electromagnetic field energy,<ref>{{Cite book |last=Feynman |first=Richard P. |title=The Feynman lectures on physics. Volume 1: Mainly mechanics, radiation, and heat |date=2011 |publisher=Basic Books |isbn=978-0-465-04085-8 |edition=The new millennium edition, paperback first published |location=New York |chapter=27–4 The ambiguity of the field energy |chapter-url=https://www.feynmanlectures.caltech.edu/II_27.html |access-date=2024-09-05 |archive-date=2024-10-03 |archive-url=https://web.archive.org/web/20241003194754/https://www.feynmanlectures.caltech.edu/II_27.html |url-status=live }}</ref> and the mechanism by which some organisms can sense [[electroreception|electric]] and [[magnetoreception|magnetic]] fields.

==Extension to nonlinear phenomena==
The Maxwell equations are ''linear,'' in that a change in the sources (the charges and currents) results in a proportional change of the fields. [[Nonlinear system|Nonlinear dynamics]] can occur when electromagnetic fields couple to matter that follows nonlinear dynamical laws.<ref>{{Cite journal |last1=Jufriansah |first1=Adi |last2=Hermanto |first2=Arief |last3=Toifur |first3=Moh. |last4=Prasetyo |first4=Erwin |date=2020-05-18 |title=Theoretical study of Maxwell's equations in nonlinear optics |journal=AIP Conference Proceedings |volume=2234 |issue=1 |pages=040013 |doi=10.1063/5.0008179 |bibcode=2020AIPC.2234d0013J |s2cid=219451710 |issn=0094-243X|doi-access=free }}</ref> This is studied, for example, in the subject of [[magnetohydrodynamics]], which combines Maxwell theory with the [[Navier–Stokes equations]].<ref>{{Cite thesis |title=Some aspects of magnetohydrodynamics |url=https://www.repository.cam.ac.uk/handle/1810/254713 |publisher=University of Cambridge |date=1967-07-27 |degree=Thesis |doi=10.17863/cam.14141 |language=en |first=Julian C. R. |last=Hunt |access-date=2022-08-22 |archive-date=2022-08-22 |archive-url=https://web.archive.org/web/20220822114814/https://www.repository.cam.ac.uk/handle/1810/254713 |url-status=live }}</ref> Another branch of electromagnetism dealing with nonlinearity is [[nonlinear optics]].

==Quantities and units==
{{see also|List of physical quantities|List of electromagnetism equations}}
Here is a list of common units related to electromagnetism:<ref>{{Cite web |title=Essentials of the SI: Base & derived units |url=https://physics.nist.gov/cuu/Units/units.html |access-date=2022-08-22 |website=physics.nist.gov |date=12 April 2010 |archive-date=2020-12-28 |archive-url=https://web.archive.org/web/20201228002022/https://physics.nist.gov/cuu/Units/units.html |url-status=live }}</ref>
{{Div col}}
* [[ampere]] (electric current, [[SI]] unit)
* [[coulomb]] (electric charge)
* [[farad]] (capacitance)
* [[henry (unit)|henry]] (inductance)
* [[ohm]] (resistance)
* [[siemens (unit)|siemens]] (conductance)
* [[tesla (unit)|tesla]] (magnetic flux density)
* [[volt]] (electric potential)
* [[watt]] (power)
* [[weber (unit)|weber]] (magnetic flux)
{{Div col end}}
In the electromagnetic [[CGS]] system, electric current is a fundamental quantity defined via [[Ampère's law]] and takes the [[Permeability (electromagnetism)|permeability]] as a dimensionless quantity (relative permeability) whose value in vacuum is [[one|unity]].<ref>{{Cite journal |date=April 1921 |title=Tables of Physical and Chemical Constants, and some Mathematical Functions |journal=Nature |language=en |volume=107 |issue=2687 |pages=264 |doi=10.1038/107264c0 |bibcode=1921Natur.107R.264. |issn=1476-4687|doi-access=free }}</ref> As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.

{{SI electromagnetism units}}

Formulas for physical laws of electromagnetism (such as [[Maxwell's equations]]) need to be adjusted depending on what system of units one uses. This is because there is no [[one-to-one correspondence]] between electromagnetic units in SI and those in CGS, as is the case for mechanical units. Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including [[Gaussian units|Gaussian]], "ESU", "EMU", and [[Heaviside–Lorentz]]. Among these choices, Gaussian units are the most common today, and in fact the phrase "CGS units" is often used to refer specifically to [[Gaussian units|CGS-Gaussian units]].<ref>{{Cite web|title=Conversion of formulae and quantities between unit systems|url=http://nlpc.stanford.edu/nleht/Science/reference/conversion.pdf|access-date=29 January 2022|website=www.stanford.edu|archive-date=5 October 2022|archive-url=https://web.archive.org/web/20221005080303/https://nlpc.stanford.edu/nleht/Science/reference/conversion.pdf|url-status=dead}}</ref>

== Applications ==
The study of electromagnetism informs [[Electrical network|electric circuits]], [[magnetic circuit]]s, and [[semiconductor device]]s' construction.

==See also==
{{Div col|colwidth=25em}}
* [[Abraham–Lorentz force]]
* [[Aeromagnetic survey]]s
* [[Computational electromagnetics]]
* [[Double-slit experiment]]
* [[Electrodynamic droplet deformation]]
* [[Electromagnet]]
* [[Electromagnetic induction]]
* [[Electromagnetic wave equation]]
* [[Electromagnetic scattering]]
* [[Electromechanics]]
* [[Geophysics]]
* [[Introduction to electromagnetism]]
* [[Magnetostatics]]
* [[Magnetoquasistatic field]]
* [[Optics]]
* [[Relativistic electromagnetism]]
* [[Wheeler–Feynman absorber theory]]
{{Div col end}}

==References==
{{reflist}}

==Further reading==
{{Library resources box
|by=no
|onlinebooks=no
|others=no
|about=yes
|label=Electromagnetism
}}

===Web sources===
{{Refbegin}}
* {{cite web
  | last = Nave
  | first = R.
  | title = Electricity and magnetism
  | url = http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon
  | website = HyperPhysics
  | publisher = Georgia State University
  | access-date = 2013-11-12
  | archive-date = 2023-06-07
  | archive-url = https://web.archive.org/web/20230607220406/http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon
  | url-status = live
  }}
* {{cite web
  | last = Khutoryansky
  | first = E.
  | title = Electromagnetism – Maxwell's Laws
  | website = [[YouTube]]
  | date = 28 December 2014
  | url = https://www.youtube.com/watch?v=9Tm2c6NJH4Y
  | access-date = 2014-12-28
  | archive-date = 2024-10-03
  | archive-url = https://web.archive.org/web/20241003194948/https://www.youtube.com/watch?v=9Tm2c6NJH4Y
  | url-status = live
  }}
{{Refend}}

===Textbooks===
{{Refbegin}}
* {{cite book|title=Electricity and Modern Physics |edition=2nd|author=G.A.G. Bennet|publisher=Edward Arnold (UK)|year=1974|isbn=978-0-7131-2459-0}}
* {{cite book|author=Browne, Michael | title= Physics for Engineering and Science |edition=2nd | publisher= McGraw-Hill/Schaum| year= 2008 | isbn=978-0-07-161399-6}}
* {{cite book | last = Dibner | first = Bern | title = Oersted and the discovery of electromagnetism | publisher = Literary Licensing, LLC | year = 2012 | isbn =978-1-258-33555-7}}
* {{cite book |author1=Durney, Carl H.  |author2=Johnson, Curtis C. | title=Introduction to modern electromagnetics | publisher=McGraw-Hill |year=1969 |isbn=978-0-07-018388-9}}
* {{cite book |author=Feynman, Richard P. |title=The Feynman Lectures on Physics Vol II |publisher=Addison Wesley Longman |year=1970 |isbn=978-0-201-02115-8 |url=https://feynmanlectures.caltech.edu/II_toc.html |access-date=2022-05-01 |archive-date=2024-10-03 |archive-url=https://web.archive.org/web/20241003195531/https://www.feynmanlectures.caltech.edu/II_toc.html |url-status=live }}
* {{cite book|last=Fleisch|first=Daniel|title=A Student's Guide to Maxwell's Equations|year=2008|publisher=Cambridge University Press|location=Cambridge, UK|isbn=978-0-521-70147-1}}
* {{cite book|title=Electromagnetism|url=https://archive.org/details/electromagnetism0000gran|url-access=registration|edition=2nd|author1=I.S. Grant|author2=W.R. Phillips|author3=Manchester Physics|publisher=John Wiley & Sons|year=2008|isbn=978-0-471-92712-9}}
* {{cite book | last = Griffiths | first = David J. | title = Introduction to Electrodynamics | edition = 3rd | publisher = Prentice Hall | year = 1998 | isbn = 978-0-13-805326-0 | author-link = David J. Griffiths | url = https://archive.org/details/introductiontoel00grif_0 }}
* {{cite book | last = Jackson | first = John D. | title = Classical Electrodynamics | url = https://archive.org/details/classicalelectro0000jack_e8g9 | url-access = registration | author-link = John David Jackson (physicist) | edition = 3rd | publisher = Wiley | year = 1998 | isbn = 978-0-471-30932-1 }}
* {{cite book| last =Moliton| first =André| title =Basic electromagnetism and materials| publisher =Springer-Verlag New York| year =2007| location =New York| url =https://books.google.com/books?id=2kPAIlxjDJwC&q=fundamental| isbn =978-0-387-30284-3}}
* {{cite book | author=Purcell, Edward M. | author-link = Edward Mills Purcell | title=Electricity and Magnetism Berkeley, Physics Course Volume 2 (2nd ed.) | publisher=McGraw-Hill | year=1985 | isbn=978-0-07-004908-6}}
* {{cite book | author=Purcell, Edward M and Morin, David. | title=Electricity and Magnetism, 820p| edition= 3rd | publisher= Cambridge University Press, New York.| year = 2013 | isbn= 978-1-107-01402-2}}
* {{cite book | author=Rao, Nannapaneni N. | title=Elements of engineering electromagnetics (4th ed.)| publisher=Prentice Hall |year=1994 |isbn=978-0-13-948746-0}}
* {{cite book | last1 = Rothwell | first1 = Edward J. | last2 = Cloud |first2=Michael J. | title = Electromagnetics | publisher = CRC Press | year = 2001 | isbn = 978-0-8493-1397-4}}
* {{cite book | last = Tipler | first = Paul | title = Physics for Scientists and Engineers: Vol. 2: Light, Electricity and Magnetism | edition = 4th | publisher = W.H. Freeman | year = 1998 | isbn = 978-1-57259-492-0}}
* {{cite book | last1 = Wangsness | first1 = Roald K. | last2 = Cloud |first2=Michael J. | title = Electromagnetic Fields | publisher = Wiley | year = 1986 | isbn = 978-0-471-81186-2| edition = 2nd }}
{{Refend}}

===General coverage===
{{Refbegin}}
* {{cite book|title=Concepts of Modern Physics|edition=4th|author=A. Beiser|publisher=McGraw-Hill (International)|year=1987|isbn=978-0-07-100144-1}}
* {{cite book|title=Physics with Modern Applications|author=L.H. Greenberg|publisher=Holt-Saunders International W.B. Saunders and Co|year=1978|isbn=978-0-7216-4247-5|url-access=registration|url=https://archive.org/details/physicswithmoder0000gree}}
* {{cite book|pages=12–13|author1=R.G. Lerner |author1-link=Rita G. Lerner|author2=G.L. Trigg | title=Encyclopaedia of Physics| publisher=VHC Publishers, Hans Warlimont, Springer|edition=2nd| year=2005| isbn=978-0-07-025734-4}}
* {{cite book|title=Principles of Physics|author1=J.B. Marion |author2=W.F. Hornyak |publisher=Holt-Saunders International Saunders College|year=1984|isbn=978-4-8337-0195-2}}
* {{cite book|title=The Physics of Vibrations and Waves|edition=3rd|author=H.J. Pain|publisher=John Wiley & Sons |year=1983|isbn=978-0-471-90182-2}}
* {{cite book| author=C.B. Parker| title=McGraw Hill Encyclopaedia of Physics| publisher=McGraw Hill| edition=2nd| year=1994| isbn=978-0-07-051400-3| url=https://archive.org/details/mcgrawhillencycl1993park}}
* {{cite book |author=R. Penrose| title=The Road to Reality| publisher= Vintage books| year=2007 | isbn=978-0-679-77631-4| title-link=The Road to Reality}}
* {{cite book|author1=P.A. Tipler |author2=G. Mosca | title=Physics for Scientists and Engineers: With Modern Physics| publisher=W.H. Freeman and Co|edition=6th| year=2008| isbn=978-1-4292-0265-7}}
* {{cite book|author1=P.M. Whelan |author2=M.J. Hodgeson | title=Essential Principles of Physics| publisher=John Murray|edition=2nd| year=1978 | isbn=978-0-7195-3382-2}}
{{Refend}}

== External links ==
{{wikiquote}}
{{Wikibooks|Electrodynamics}}
* [http://www.unitconversion.org/unit_converter/magnetic-field-strength.html Magnetic Field Strength Converter]
* [http://scienceworld.wolfram.com/physics/ElectromagneticForce.html Electromagnetic Force] – from Eric Weisstein's World of Physics

{{Fundamental interactions}}
{{Branches of physics}}
{{Magnetic states}}
{{Authority control}}

[[Category:Electromagnetism| ]]
[[Category:Electrodynamics| ]]
[[Category:Fundamental interactions]]