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Electromagnetism is a branch of
physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of eve ...

physics
involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the in ...
s composed of
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' ' ...

electric field
s and
magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with ...

magnetic field
s, and it is responsible for
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

electromagnetic radiation
such as
light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

light
. It is one of the four
fundamental interaction In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Sp ...
s (commonly called forces) in
nature Nature, in the broadest sense, is the natural, physical, material world or universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter an ...

nature
, together with the
strong interaction In nuclear physics Nuclear physics is the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and ...
, the
weak interaction In nuclear physics Nuclear physics is the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and ...
, and
gravitation Gravity (), or gravitation, is a natural phenomenon Types of natural phenomena include: Weather, fog, thunder, tornadoes; biological processes, decomposition, germination seedlings, three days after germination. Germination is th ...

gravitation
. At high energy, the weak force and electromagnetic force are unified as a single
electroweak force In particle physics, the electroweak interaction or electroweak force is the unified field theory, unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces ...
. Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the
Lorentz force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Ph ...

Lorentz force
, which includes both
electricity Electricity is the set of physical Physical may refer to: *Physical examination, a regular overall check-up with a doctor *Physical (album), ''Physical'' (album), a 1981 album by Olivia Newton-John **Physical (Olivia Newton-John song), "Physi ...

electricity
and
magnetism Magnetism is a class of physical attributes that are mediated by magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For in ...

magnetism
as different manifestations of the same phenomenon. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. The electromagnetic attraction between
atomic nuclei The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger-Marsden experiments, Geiger–Marsden gold foil experiment. After the d ...
and their orbital
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

electron
s holds
atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...

atom
s together. Electromagnetic forces are responsible for the
chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday ...
s between atoms which create
molecule A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon ...

molecule
s, and
intermolecular force An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighboring particles, e.g. atom ...

intermolecular force
s. The electromagnetic force governs all chemical processes, which arise from interactions between the
electrons The electron is a subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has m ...
of neighboring atoms. Electromagnetism is very widely used in modern technology, and electromagnetic theory is the basis of
electric power engineering
electric power engineering
and
electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons The electron is a subatomic particle In physical sciences, subatomic particles are smaller than ...
including digital technology. There are numerous
mathematical descriptions of the electromagnetic field There are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental interactions of nature. In this article, several approaches are discussed, although the equations ...
. Most prominently,
Maxwell's equations Maxwell's equations are a set of coupled partial differential equation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), ...
describe how electric and magnetic fields are generated and altered by each other and by charges and currents. The theoretical implications of electromagnetism, particularly the establishment of the speed of light based on properties of the "medium" of propagation ( permeability and
permittivity In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is car ...
), led to the development of
special relativity In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
by
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
in 1905.


History of the theory

Originally, electricity and magnetism were considered to be two separate forces. This view changed with the publication of
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In classica ...

James Clerk Maxwell
's 1873 ''
A Treatise on Electricity and Magnetism ''A Treatise on Electricity and Magnetism'' is a two-volume treatise on electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric ...
'' 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 ' or ' one another with a force
inversely proportional In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
to the square of the distance between them: unlike charges attract, like ones repel. # 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. # 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. # 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. In April 1820,
Hans Christian Ørsted Hans Christian Ørsted ( , ; often rendered Oersted in English; 14 August 17779 March 1851) was a Danish physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge ...

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. Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire. The
CGS
CGS
unit of
magnetic induction Electromagnetic or magnetic induction is the production of an electromotive force In electromagnetism and electronics, electromotive force (emf, denoted \mathcal and measured in volts) is the electrical action produced by a non-electrical sour ...

magnetic induction
(
oersted The oersted (symbol Oe) is the coherent derived unit of the auxiliary magnetic field H in the centimetre–gram–second system of units The centimetre–gram–second system of units (abbreviated CGS or cgs) is a variant of the metric syste ...
) is named in honor of his contributions to the field of electromagnetism. His findings resulted in intensive research throughout the scientific community in
electrodynamics Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is carried by electromagneti ...
. They influenced French physicist
André-Marie Ampère André-Marie Ampère (, ; ; 20 January 177510 June 1836) was a French physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of ...
'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 Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge ...

Michael Faraday
, extended by
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In classica ...

James Clerk Maxwell
, and partially reformulated by
Oliver Heaviside Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English autodidactic Autodidacticism (also autodidactism) or self-education (also self-learning and self-teaching) is education without the guidance of masters (such as teach ...
and
Heinrich Hertz Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empi ...

Heinrich Hertz
, is one of the key accomplishments of 19th-century
mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developme ...
. It has had far-reaching consequences, one of which was the understanding of the nature of
light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

light
. Unlike what was proposed by the electromagnetic theory of that time, light and other
electromagnetic waves In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...

electromagnetic waves
are at present seen as taking the form of
quantized
quantized
, self-propagating
oscillatory
oscillatory
electromagnetic field disturbances called
photon The photon ( el, φῶς, phōs, light) is a type of elementary particle In , an elementary particle or fundamental particle is a that is not composed of other particles. Particles currently thought to be elementary include the fundamental s ...

photon
s. Different
frequencies Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparent ...

frequencies
of oscillation give rise to the different forms of
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

electromagnetic radiation
, from
radio wave Radio waves are a type of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...
s at the lowest frequencies, to visible light at intermediate frequencies, to
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, it ...
s at the highest frequencies. Ørsted was not the only person to examine the relationship between electricity and magnetism. In 1802,
Gian Domenico Romagnosi Gian Domenico Romagnosi (; 11 December 1761 – 8 June 1835) was an Italian philosopher, economist and jurist. Biography Gian Domenico Romagnosi was born in Salsomaggiore Terme. He studied law at the University of Parma from 1782 to 1786. In 1 ...
, an Italian legal scholar, deflected a magnetic needle using a Voltaic pile. The factual setup of the experiment is not completely clear, so 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. An earlier (1735), and often neglected, connection between electricity and magnetism was reported by a Dr. Cookson. The account stated:
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 ...
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."


Fundamental forces

The electromagnetic force is one of the four known
fundamental force#REDIRECT Fundamental interaction In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics ...
s. The other fundamental forces are: * the
strong nuclear force In nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. Other forms of nuclear matter are also studied. Nuclear physics should not be confused with atomic physics, which ...
, which binds
quark A quark () is a type of elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include the fundam ...

quark
s to form
nucleon In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...
s, and binds nucleons to form
nuclei ''Nucleus'' (plural nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA ...
. * the
weak nuclear force In nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. Other forms of nuclear matter are also studied. Nuclear physics should not be confused with atomic physics, which ...
, which binds to all known particles in the
Standard Model The Standard Model of particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsi ...

Standard Model
, and causes certain forms of
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consi ...

radioactive decay
. (In
particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...
though, the
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction); * the
gravitational force Gravity (), or gravitation, is a natural phenomenon Types of natural phenomena include: Weather, fog, thunder, tornadoes; biological processes, decomposition, germination seedlings, three days after germination. Germination is t ...

gravitational force
. All other forces (e.g.,
friction Friction is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, st ...

friction
, contact forces) are derived from these four
fundamental forces In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Sp ...
and they are known as non-fundamental forces. The electromagnetic force is responsible for practically all phenomena one encounters in daily life above the nuclear scale, with the exception of gravity. Roughly speaking, all the forces involved in interactions between
atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...

atom
s can be explained by the electromagnetic force acting between the electrically charged
atomic nuclei The atomic nucleus is the small, dense region consisting of proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutr ...
and
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

electron
s of the atoms. Electromagnetic forces also explain how these particles carry momentum by their movement. This includes the forces we experience in "pushing" or "pulling" ordinary material objects, which result from the
intermolecular force An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighboring particles, e.g. atom ...

intermolecular force
s that act between the individual
molecule A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon ...

molecule
s in our bodies and those in the objects. The electromagnetic force is also involved in all forms of
chemical phenomena
chemical phenomena
. A necessary part of understanding the intra-atomic and intermolecular forces is the effective force generated by the momentum of the electrons' movement, such that 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 Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermion In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc ...
. The behaviour 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.


Classical electrodynamics

In 1600, William Gilbert proposed, in his ''
De Magnete Title page of 1628 edition ''De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure'' (''On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth'') is a scientific work published in 1600 by the English physician and scien ...
'', that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. 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 Benjamin Franklin ( April 17, 1790) was one of the Founding Fathers of the United States The Founding Fathers of the United States, or simply the Founding Fathers or Founders, were a group of American revolutionary Patriots (also ...

Benjamin Franklin
's proposed experiments in 1752. One of the first to discover and publish a link between man-made electric current and magnetism was
Gian Romagnosi
Gian Romagnosi
, who in 1802 noticed that connecting a wire across a
voltaic pile The voltaic pile was the first electrical battery A battery is a device consisting of one or more electrochemical cell An electrochemical cell is a device capable of either generating electrical energy from chemical reaction A che ...

voltaic pile
deflected a nearby
compass A compass is a device that shows the cardinal direction The four cardinal directions, or cardinal points, are the directions north, east, south, and west, commonly denoted by their initials N, E, S, and W. East and west are perpendicular ( ...

compass
needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment. Ørsted's work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation. A theory of electromagnetism, known as
classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and ...
, was developed by various physicists during the period between 1820 and 1873 when it culminated in the publication of a
treatise A treatise is a formal Formal, formality, informal or informality imply the complying with, or not complying with, some set theory, set of requirements (substantial form, forms, in Ancient Greek). They may refer to: Dress code and events * For ...
by
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In classica ...

James Clerk Maxwell
, which unified the preceding developments into a single theory and discovered the electromagnetic nature of light. In classical electromagnetism, the behavior of the electromagnetic field is described by a set of equations known as
Maxwell's equations Maxwell's equations are a set of coupled partial differential equation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), ...
, and the electromagnetic force is given by the
Lorentz force law Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyb ...

Lorentz force law
.Purcell: p. 278: Chapter 6.1, "Definition of the Magnetic Field." Lorentz force and force equation. 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 The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
in a vacuum is a universal constant that is dependent only on the electrical permittivity and
magnetic permeability In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is ...
of
free space A vacuum is space devoid of matter. The word stems from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicist ...
. This violates
Galilean invariance Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frame In classical physics Classical physics is a group of physics Physics (from grc, φυσική (ἐπιστήμη), physik ...
, 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 Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium Medium may refer to: Science and technology Aviation *Medium bomber, a class of war plane *Tecma Medium, a French hang glider design Communic ...
through which the light propagates. However, subsequent experimental efforts failed to detect the presence of the aether. After important contributions of
Hendrik Lorentz Lorentz' theory of electrons. Formulas for the curl of the magnetic field (IV) and the electrical field E (V), ''La théorie electromagnétique de Maxwell et son application aux corps mouvants'', 1892, p. 452. Hendrik Antoon Lorentz (; 18 Ju ...

Hendrik Lorentz
and
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French French (french: français(e), link=no) may refer to: * Something of, from, or related to France France (), officially the French Repu ...
, in 1905,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

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 The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einst ...
.) 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 The covariant formulation of classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charge Electric charge is the physical property ...
.)


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 dynamics In mathematics and science, a nonlinear system is a system in which the change of the output is not proportionality (mathematics), proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, ...
can occur when electromagnetic fields couple to matter that follows nonlinear dynamical laws. This is studied, for example, in the subject of
magnetohydrodynamics Magnetohydrodynamics (MHD; also magneto-fluid dynamics or hydro­magnetics) is the study of the magnetic properties and behaviour of electrically conducting Electrical resistivity (also called specific electrical resistance or volume res ...
, which combines Maxwell theory with the
Navier–Stokes equations In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
.


Quantities and units

Electromagnetic units are part of a system of electrical units based primarily upon the magnetic properties of electric currents, the fundamental SI unit being the ampere. The units are: *
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particle In physics ...

ampere
(electric current) *
coulomb The coulomb (symbol: C) is the International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' ( ...

coulomb
(electric charge) *
farad The farad (symbol: F) is the SI derived unit of electrical capacitance, the ability of a body to store an electrical charge. It is named after the English physicist Michael Faraday (1791-1867). In SI base units 1 F = 1 kilogram, kg− ...
(capacitance) *
henry Henry may refer to: People *Henry (given name) Henry is a masculine given name derived from Old French Old French (, , ; French language, Modern French: ) was the language spoken in Northern France from the 8th century to the 14th century ...
(inductance) *
ohm The ohm (symbol: Ω) is the SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, ...

ohm
(resistance) *
siemens Siemens AG ( ) is a German multinational Multinational may refer to: * Multinational corporation, a corporate organization operating in multiple countries * Multinational force, a military body from multiple countries * Multinational state, ...
(conductance) * tesla (magnetic flux density) *
volt The volt is the derived unit for electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

volt
(electric potential) *
watt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...

watt
(power) *
weber Weber (, or ; German: ) is a surname of German language, German origin, derived from the noun meaning "weaving, weaver". In some cases, following migration to English-speaking countries, it has been anglicised to the English surname 'Webber' or ev ...
(magnetic flux) In the electromagnetic cgs system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in a vacuum is
unity Unity may refer to: Buildings * Unity Building The Unity Building, in Oregon, Illinois, is a historic building in that city's Oregon Commercial Historic District. As part of the district the Oregon Unity Building has been listed on the National R ...

unity
. As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system. Formulas for physical laws of electromagnetism (such as
Maxwell's equations Maxwell's equations are a set of coupled partial differential equation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), ...
) need to be adjusted depending on what system of units one uses. This is because there is no
one-to-one correspondence In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
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 Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymous ...
, "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 CGS-Gaussian units.


See also

*
Abraham–Lorentz force In the physics of electromagnetism, the Abraham–Lorentz force (also Lorentz–Abraham force) is the recoil force on an acceleration, accelerating charged particle caused by the particle emitting electromagnetic radiation. It is also called the ra ...
*
Aeromagnetic survey An aeromagnetic survey is a common type of geophysical survey Geophysical survey is the systematic collection of geophysical data for spatial studies. Detection and analysis of the geophysical signals forms the core of Geophysical signal process ...
s *
Computational electromagnetics Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment. It typically involves using computer p ...
*
Double-slit experiment In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechani ...
*
Electromagnet An electromagnet is a type of magnet A magnet is a material or object that produces a magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each poin ...

Electromagnet
*
Electromagnetic induction Electromagnetic or magnetic induction is the production of an electromotive force In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs b ...

Electromagnetic induction
*
Electromagnetic wave equation The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a Medium (optics), medium or in a vacuum. It is a Wave equation#Scalar wave equation in three space d ...
*
Electromagnetic scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light Light or visible light is electromagnetic radiation within the portion of the electromagneti ...
*
Electromechanics In engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encomp ...
*
Geophysics Geophysics () is a subject of natural science Natural science is a branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , plant biology or phytology, is the science of plant life and a b ...

Geophysics
* Introduction to electromagnetism *
Magnetostatics Magnetostatics is the study of magnetic fields in systems where the electric currents, currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the electric charge, charges are stationary. The magnetizati ...
*
Magnetoquasistatic field A magnetoquasistatic field is a class of electromagnetic field in which a slowly oscillating magnetic field is dominant. A magnetoquasistatic field is typically generated by ''low-frequency'' induction from a magnetic dipole or a current loop. The ...
*
Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

Optics
*
Relativistic electromagnetism Relativistic electromagnetism is a physical phenomenon explained in electromagnetic field theory due to Coulomb's law ''F'' between two point charges ''q''1 and ''q''2 is directly proportional to the product of the magnitudes of charges and ...
*
Wheeler–Feynman absorber theory The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theor ...


References


Further reading


Web sources

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Textbooks

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General references

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External links


Magnetic Field Strength Converter


– from Eric Weisstein's World of Physics * {{Authority control