{{Short description|Fundamental interaction between charged particles}}
{{Pp-semi-indef}}
{{For introduction}}
{{hatnote group|
{{Redirect|Electromagnetics|the academic journal|Electromagnetics (journal){{!}}''Electromagnetics'' (journal)}}
{{Redirect|Electromagnetic force|the force exerted on particles by electromagnetic fields|Lorentz force}}
{{Redirect-synonym|Electromagnetic|the use of an [[electromagnet]]}}
}}
{{Electromagnetism|cTopic=-}}
{{TopicTOC-Physics|Branches}}

In [[physics]], '''electromagnetism''' is an interaction that occurs between [[particles]] with [[electric charge]] via [[electromagnetic field]]s. 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 describes and relates the three distinct but closely intertwined phenomena of [[electricity]], [[magnetism]], and [[optics]]. In the study of electromagnetism these phenomena are described by the  3 sub-disciplines: [[electrostatics]], [[magnetostatics]], and [[electrodynamics]].

The electromagnetic force is responsible for many [[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. 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 to explain the electric phenomena of [[lightning]] and [[static electricity]] and the magnetic phenomenon of the attraction between magnetized pieces of [[iron ore]] and of [[compass]]es. In the 18th and 19th centuries scientists developed the mathematical relationships between these phenomena and [[electric charge]]s and [[electric current|currents]]. They also showed that electrical and magnetic phenomena were related and could create a self-sustaining [[electromagnetic waves]] which forms [[visible light]] and other forms of [[electromagnetic radiation]] including [[Gamma-rays]], [[x-rays]], [[ultraviolet]], visible, [[infrared]] radiation, [[microwave]]s and [[radio wave]]s.

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.

Mathematically, electromagnetism is described by [[electromagnetic field]]s. These are quantities that describe the electrical ([[electric field]]) and magnetic ([[magnetic field]]) influence at a given location and time.

== A fundamental force ==
{{main|Fundamental forces}}

[[File:Plasma globe 60th.jpg|thumb|300x300px|Electromagnetic interactions are responsible for the glowing filaments in this [[plasma globe]].]]
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. |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]].

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>
==Electromagnetic fields==
{{main|electromagnetic field}}

The phenomena of electromagnetism is described mathematically using electromagnetic fields. An electromagnetic field (also '''EM field''') is a [[physical field]], varying in space and time, that represents the electric and magnetic influences generated by and acting upon [[electric charge]]s. The field at any point in space and time can be regarded as a combination of an [[electric field]] and a [[magnetic field]]. Because of the interrelationship between the fields, a disturbance in the electric field can create a disturbance in the magnetic field which in turn affects the electric field, leading to an oscillation that propagates through space, known as an ''[[electromagnetic wave]]''.

There are 6 mathematical quantities which are used to describe electromagnetic fields in 3 distinct cases. The [[electric field]], {{math|'''E'''}}, and [[magnetic flux density]], {{math|'''B'''}} are used to describe the electromagnetic fields in cases where all the charges are known directly such as the electromagnetic field in a vacuum. To describe the case where the charges inside of a material respond to applied electric and magnetic fields, it is useful to define the [[electric displacement field]], {{math|'''D'''}} and [[magnetic field strength]], {{math|'''H'''}}, in addition to {{math|'''E'''}} and {{math|'''B'''}}. Finally, it is sometimes useful to describe electromagnetic fields not in terms of force but in terms of potential energy and momentum. In this case, the electromagnetic field is represented by the [[electric potential]], {{math|V}}, and the [[magnetic vector potential]], {{math|'''A'''}}, respectively.

[[File:Lorentz force particle.svg|thumb|Lorentz force {{math|'''F'''}} on a [[charged particle]] (of charge {{mvar|q}}) in motion (instantaneous velocity {{math|'''v'''}}). The [[electric field|{{math|'''E'''}} field]] and [[magnetic field|{{math|'''B'''}} field]] vary in space and time.]]
===Force on an electric charge due to electromagnetic fields===

{{main|Lorentz force}}
The force, {{math|'''F'''}}. on a charge particle of charge {{math|q}} moving at speed {{math|'''v'''}} in an electromagnetic field is given by the Lorentz force([[SI]] definition of quantities{{efn|In SI units, {{math|'''B'''}} is measured in [[tesla (unit)|teslas]] (symbol: T). In [[Gaussian units|Gaussian-cgs units]], {{math|'''B'''}} is measured in [[gauss (unit)|gauss]] (symbol: G).<ref>{{cite web | url=https://www.ncei.noaa.gov/products/geomagnetism-frequently-asked-questions | title=Geomagnetism Frequently Asked Questions | publisher=National Geophysical Data Center | access-date=21 October 2013}})</ref> {{math|'''H'''}} is measured in [[ampere]]s per metre (A/m) in SI units, and in [[oersted]]s (Oe) in cgs units.<ref>{{cite web | title=International system of units (SI) |url=http://physics.nist.gov/cuu/Units/units.html | work=NIST reference on constants, units, and uncertainty |date=12 April 2010 | publisher=National Institute of Standards and Technology | access-date=9 May 2012}}</ref>}}):{{sfn|Jackson|1998|pp=2-3}}
<math>\mathbf{F} = q \left(\mathbf{E} + \mathbf{v} \times \mathbf{B}\right)</math>

Here, {{math|×}} is the vector [[cross product]], and all quantities in bold are vectors.

The Lorentz force can be used to define both the electric field {{math|'''E'''}} and the magnetic flux density {{math|'''B'''}}.

===Electromagnetic fields in matter===

{{main|electric displacement field|magnetic field strength}}

When dealing with electromagnetic fields in matter it is often useful to introduce 2 other fields, in addition to {{math|'''E'''}} and {{math|'''B'''}}. Since matter is made of particles with both electric charge and intrinsic [[magnetic moment]] it responds to an applied electromagnetic field to produce its own electromagnetic field. The details are complicated but often can be described by introducing an [[electric displacement field]], {{math|'''D'''}} to complement {{math|'''E'''}} and a [[magnetic field strength]], {{math|'''H'''}}, to complement {{math|'''B'''}}.

===Electric potential formulation===

{{main|electric potential|magnetic vector potential}}

In advanced formulations of electromagnetism and to simplify certain calculations it is often useful to reformulate the electromagnetic field in terms of electric potential energy and momentum instead of force. Here, the electromagnetic fields of interest are the electric potential, {{math|V}}, and the magnetic vector potential {{math|'''A'''}}. These are related to {{math|'''E'''}} and {{math|'''B'''}} by:
<math display="block">\begin{align}
 \mathbf{E} &= - \nabla V - \frac { \partial \mathbf{A} } { \partial t } \\[1ex]
 \mathbf{B} &= \nabla \times \mathbf{A}
\end{align}</math>
where {{math|∇}} is the gradient, {{math|∇⋅}} is the divergence, and {{math|∇×}} is the [[Curl (mathematics)|curl]].

==Electrostatics==
{{main|electrostatics}}

[[File:Cat demonstrating static cling with styrofoam peanuts.jpg|thumb|upright=1.3|alt=A tabby cat covered in packing peanuts.|[[Foam peanut]]s clinging to a cat's fur due to [[static electricity]]. The cat's fur becomes charged due to the [[triboelectricity|triboelectric effect]]. The electric field of the charged fur causes polarization of the molecules of the foam due to [[electrostatic induction]], resulting in a slight attraction of the light plastic pieces to the fur.<ref name="Ling">
{{cite book |last1=Ling |first1=Samuel J. |url=https://openstax.org/books/university-physics-volume-2/pages/5-2-conductors-insulators-and-charging-by-induction |title=University Physics, Vol. 2 |last2=Moebs |first2=William |last3=Sanny |first3=Jeff |date=2019 |publisher=OpenStax |isbn=9781947172210 |doi= |id=}} Ch.30: Conductors, Insulators, and Charging by Induction</ref><ref name="Bloomfield">
{{cite book
 | last1  = Bloomfield
 | first1 = Louis A.
 | title  = How Things Work: The Physics of Everyday Life
 | publisher = John Wiley and Sons
 | date   = 2015
 | pages  = 270
 | url    = https://books.google.com/books?id=TLE7CwAAQBAJ&dq=polarization&pg=PA270
 | doi    =
 | id     =
 | isbn   = 9781119013846
}}</ref><ref name="PhysicsClassroom">
{{cite web
 | title = Polarization
 | work = Static Electricity – Lesson 1 – Basic Terminology and Concepts
 | publisher = The Physics Classroom
 | date = 2020
 | url = https://www.physicsclassroom.com/class/estatics/u8l1e.cfm
 | format =
 | doi =
 | accessdate = 18 June 2021}}</ref><ref name="Thompson">{{cite web
 | last = Thompson
 | first = Xochitl Zamora
 | title = Charge It! All About Electrical Attraction and Repulsion
 | work = Teach Engineering: Stem curriculum for K-12
 | publisher = University of Colorado
 | date = 2004
 | url = https://www.teachengineering.org/activities/view/cub_electricity_lesson02_activity1
 | format =
 | doi =
 | accessdate = 18 June 2021
}}</ref> This effect is also the cause of [[static cling]] in clothes.]]

'''Electrostatics''' is a branch of [[physics]] that studies slow-moving or stationary [[electric charge]]s on macroscopic objects where [[quantum mechanics|quantum]] effects can be neglected. Under these circumstances, the electric field, electric potential, and the charge density are related without complications from magnetic effects.

Since [[classical antiquity]], it has been known that some materials, such as [[amber]], attract lightweight particles after [[triboelectric effect|rubbing]].<ref name="Brockman 1929">{{cite journal |last1=Brockman |first1=C.J. |title=The history of electricity before the discovery of the voltaic pile |journal=Journal of Chemical Education |date=October 1929 |volume=6 |issue=10 |pages=1726-1732 |doi=10.1021/ed006p1726}}</ref> The [[Greek language|Greek]] word {{Transliteration|el|ḗlektron}} ({{lang|el|ἤλεκτρον}}), meaning 'amber', was thus the [[Root (linguistics)|root]] of the word ''[[electricity]]''. Electrostatic phenomena arise from the [[force]]s that electric charges exert on each other. Such [[forces]] are described by [[Coulomb's law]].

There are many examples of electrostatic phenomena, from those as simple as the attraction of plastic wrap to one's hand after it is removed from a package, to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and [[photocopier]] and [[laser printing|laser printer]] operation.

==Magnetostatics==
{{main|magnetostatics}}
'''Magnetostatics''' is the study of [[magnetic field]]s in systems where the [[electric currents|currents]] are [[steady current|steady]] (not changing with time). It is the magnetic analogue of [[electrostatics]], where the [[electric charge|charges]] are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast [[Magnetization reversal|magnetic switching]] events that occur on time scales of nanoseconds or less.<ref name="Hiebert">{{cite journal |last1=Hiebert |first1=W |last2=Ballentine |first2=G |last3=Freeman |first3=M |title=Comparison of experimental and numerical micromagnetic dynamics in coherent precessional switching and modal oscillations |journal = [[Physical Review B]] |volume=65 |number=14 |article-number=140404 |year=2002 |doi=10.1103/PhysRevB.65.140404 |bibcode=2002PhRvB..65n0404H }}</ref> Magnetostatics is even a good approximation when the currents are not static &ndash; as long as the currents do not [[alternating current|alternate]] rapidly. Magnetostatics is widely used in applications of [[micromagnetics]] such as models of [[magnetic storage]] devices as in [[computer memory]].

==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 |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! &#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 }}{{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>

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 2: Mainly electromagnetism and matter |date=2011 |publisher=Basic Books |isbn=978-0-465-04085-8 |location=New York |chapter=27–4 The ambiguity of the field energy |chapter-url=https://www.feynmanlectures.caltech.edu/II_27.html#Ch27-S4}}</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 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==
{{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 |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}}

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 ==
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}}

==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 |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===
[[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 |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 ([[Coulomb's law]]): 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 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 />
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}}
==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}}

==Notes==
{{notelist}}

==References==

{{reflist}}

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

===Web sources===
{{Refbegin}}
* {{cite web
  | last = Tong
  | first = David
  | title = Electromagnetism
  | url = https://davidtong.org/teaching/electromagnetism/
  | website = davidtong.org
  | publisher = University of Cambridge
  }}
* {{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}}
* {{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|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 | 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|author=Weng Cho Chew |title=Lectures on Electromagnetic Field Theory: A Comprehensive Overview |publisher=Purdue University Press |year=2025 |url=https://muse.jhu.edu/book/148137 |isbn=9781626710979}}
{{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]
* [https://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]]