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{{Electromagnetism|cTopic=-}} | {{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. 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. | 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 news |last1=Biggs |first1=Ben |last2=published |first2=Jeremy Rehm |title=The four fundamental forces of nature |url=https://www.space.com/four-fundamental-forces.html |work=Space |date=23 December 2021 }}</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. | 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. | ||
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===Ancient world=== | ===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">{{ | 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 |title=Knowledge of magnetism in ancient Mesoamerica: Precision measurements of the potbelly sculptures from Monte Alto, Guatemala |journal=Journal of Archaeological Science |date=June 2019 |volume=106 |pages=29–36 |doi=10.1016/j.jas.2019.03.001 |bibcode=2019JArSc.106...29F }}</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>{{cite book |last1=Du Trémolet De Lacheisserie |first1=É. |last2=Gignoux |first2=D. |last3=Schlenker |first3=M. |title=Magnetism |chapter=Magnetism, from the Dawn of Civilization to Today |date=2002 |pages=3–18 |doi=10.1007/978-0-387-23062-7_1 |isbn=978-1-4020-7222-2 }}</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=== | ===19th century=== | ||
[[File:A Treatise on Electricity and Magnetism Volume 2 003.jpg|thumb|Cover of ''A Treatise on Electricity and Magnetism'']] | [[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>{{ | 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 |title=A Treatise on Electricity and Magnetism |journal=Nature |date=1873 |volume=7 |issue=182 |pages=478–480 |doi=10.1038/007478a0 |bibcode=1873Natur...7..478. }}</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> | # 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> | # 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 >{{ | # 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 news |last1=Lucas |first1=Jim |title=What Is Faraday's Law of Induction? |url=https://www.livescience.com/53509-faradays-law-induction.html |work=Live Science |date=18 February 2022 }}</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 /> | # 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>{{ | 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 |title=History of the Electric Telegraph |journal=Scientific American |date=1884 |volume=17 |issue=425supp |pages=6784–6786 |doi=10.1038/scientificamerican02231884-6784supp }}</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}}{{pn|date=April 2026}}</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}}{{pn|date=April 2026}}</ref> His findings influenced French physicist [[André-Marie Ampère]]'s developments of a single mathematical form to represent the magnetic forces between current-carrying conductors.<ref name="WhittakerET">[[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 19th century]]. Dublin University Press series. London: Longmans, Green and Co.; [etc.].</ref> | ||
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 }}{{pn|date=April 2026}}</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.{{fact|date=April 2026}} | |||
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. | |||
== A fundamental force == | == 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]] | [[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" | 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>{{ | 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. |title=Electromagnetic and weak interactions |journal=Physics Letters |date=1964 |volume=13 |issue=2 |pages=168–171 |doi=10.1016/0031-9163(64)90711-5 |bibcode=1964PhL....13..168S }}</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]]. | 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]]. | ||
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{{Main|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>{{ | 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 |title=Gilbert's de Magnete: An early study of magnetism and electricity |journal=Eos, Transactions American Geophysical Union |date=2000 |volume=81 |issue=21 |pages=233–234 |doi=10.1029/00EO00163 |bibcode=2000EOSTr..81..233M }}</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! | 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 }}{{pn|date=April 2026}}</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> | 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> | ||
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==Extension to nonlinear phenomena== | ==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>{{ | 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 book |last1=Jufriansah |first1=Adi |last2=Hermanto |first2=Arief |last3=Toifur |first3=Moh. |last4=Prasetyo |first4=Erwin |title=CONFERENCE ON THEORETICAL PHYSICS AND NONLINEAR PHENOMENA (CTPNP) 2019: Excursion from Vacuum to Condensed Matter |chapter=Theoretical study of Maxwell's equations in nonlinear optics |date=2020 |volume=2234 |page=040013 |doi=10.1063/5.0008179 }}</ref> This is studied, for example, in the subject of [[magnetohydrodynamics]], which combines Maxwell theory with the [[Navier–Stokes equations]].<ref>{{cite thesis |last1=Hunt |first1=Julian C. R. |title=Some aspects of magnetohydrodynamics |date=2016 |publisher=Apollo - University of Cambridge Repository |doi=10.17863/cam.14141 }}{{pn|date=April 2026}}</ref> Another branch of electromagnetism dealing with nonlinearity is [[nonlinear optics]]. | ||
==Quantities and units== | ==Quantities and units== | ||
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* [[weber (unit)|weber]] (magnetic flux) | * [[weber (unit)|weber]] (magnetic flux) | ||
{{Div col end}} | {{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>{{ | 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 |title=Tables of Physical and Chemical Constants, and some Mathematical Functions |journal=Nature |date=1921 |volume=107 |issue=2687 |page=264 |doi=10.1038/107264c0 |bibcode=1921Natur.107R.264. }}</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}} | {{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>{{ | 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 report |first1=Nikolai G. |last1=Lehtinen |date=4 November 2010 |title=Conversion of formulae and quantities between unit systems |url=http://nlpc.stanford.edu/nleht/Science/reference/conversion.pdf |access-date=29 January 2022 |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 }}{{self-published inline|date=April 2026}}</ref> | ||
== Applications == | == Applications == | ||
The | The theory of electromagnetism is used to understand and design [[Electrical network|electric circuits]], [[magnetic circuit]]s, and [[semiconductor device]]s.{{fact|date=April 2026}} | ||
==See also== | ==See also== | ||
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* {{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 | 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 |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 | * {{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}} | ||
* {{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|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|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}} | ||
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* {{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=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 | 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|author1-link=Edward Rothwell (engineer)| 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 | 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 }} | * {{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 }} | ||