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Electromagnetism
Electromagnetism
Electromagnetism
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Electromagnetic interactions are responsible for the glowing filaments in this plasma globe.
Electromagnetism
Solenoid
Electrostatics
Magnetostatics
Electrodynamics
Electrical network
Magnetic circuit
Covariant formulation
Scientists

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

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

In the modern era, scientists continue to refine the theory of electromagnetism to account for the effects of modern physics, including quantum mechanics and 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 and permittivity), helped inspire Einstein's theory of special relativity in 1905. Quantum electrodynamics (QED) modifies Maxwell's equations to be consistent with the quantized nature of matter. In QED, changes in the electromagnetic field are expressed in terms of discrete excitations, particles known as photons, the quanta of light.

History

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Main article: History of electromagnetic theory

Ancient world

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Investigation into electromagnetic phenomena began about 5,000 years ago. There is evidence that the ancient Chinese,[2] Mayan,[3][4] and potentially even Egyptian civilizations knew that the naturally magnetic mineral magnetite had attractive properties, and many incorporated it into their art and architecture.[5] Ancient people were also aware of lightning and static electricity, although they had no idea of the mechanisms behind these phenomena. The 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).[6]

19th century

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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[7] 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:

  1. Electric charges attract or repel one another with a force inversely proportional to the square of the distance between them: opposite charges attract, like charges repel.[8]
  2. 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.[9]
  3. 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.[10]
  4. 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.[10]

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.[11][12] 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 magnetic induction (oersted) is named in honor of his contributions to the field of electromagnetism.[13]

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

This unification, which was observed by Michael Faraday, extended by James Clerk Maxwell, and partially reformulated by Oliver Heaviside and Heinrich Hertz, is one of the key accomplishments of 19th-century mathematical physics.[14] 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 quantized, self-propagating oscillatory electromagnetic field disturbances called photons. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies.

Ørsted was not the only person to examine the relationship between electricity and magnetism. In 1802, Gian Domenico Romagnosi, an Italian legal scholar, deflected a magnetic needle using a Voltaic pile. The factual setup of the experiment is not completely clear, nor if current flowed across the needle or not. An account of the discovery was published in 1802 in an Italian newspaper, but it was largely overlooked by the contemporary scientific community, because Romagnosi seemingly did not belong to this community.[15]

An earlier (1735), and often neglected, connection between electricity and magnetism was reported by a Dr. Cookson.[16] 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."[17]

A fundamental force

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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.[18] All other forces, known as non-fundamental forces.[19] (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.[20]

Most of the forces involved in interactions between atoms are explained by electromagnetic forces between electrically charged atomic nuclei and electrons. The electromagnetic force is also involved in all forms of 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 forces between individual molecules 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.[21]

Classical electrodynamics

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Main article: Classical electrodynamics

In 1600, William Gilbert proposed, in his De Magnete, that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects.[22] 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 May 1752 by Thomas-François Dalibard of France using a 40-foot-tall (12 m) iron rod instead of a kite and he successfully extracted electrical sparks from a cloud.[23][24]

One of the first to discover and publish a link between human-made electric current and magnetism was 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.[25] 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.[26]

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 treatise was published, which unified previous developments into a single theory, proposing that light was an electromagnetic wave propagating in the luminiferous ether.[27] 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.[28]

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,[29] and the mechanism by which some organisms can sense electric and magnetic fields.

Extension to nonlinear phenomena

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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 can occur when electromagnetic fields couple to matter that follows nonlinear dynamical laws.[30] This is studied, for example, in the subject of magnetohydrodynamics, which combines Maxwell theory with the Navier–Stokes equations.[31] Another branch of electromagnetism dealing with nonlinearity is nonlinear optics.

Quantities and units

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See also: List of physical quantities and List of electromagnetism equations

Here is a list of common units related to electromagnetism:[32]

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 vacuum is unity.[33] 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
Symbol[34] Name of quantity Unit name Symbol Base units
E energy joule J = C⋅V = W⋅s kg⋅m2⋅s−2
Q electric charge coulomb C A⋅s
I electric current ampere A = C/s = W/V A
J electric current density ampere per square metre A/m2 A⋅m−2
U, ΔV; Δϕ; E, ξ potential difference; voltage; electromotive force volt V = J/C kg⋅m2⋅s−3⋅A−1
R; Z; X electric resistance; impedance; reactance ohm Ω = V/A kg⋅m2⋅s−3⋅A−2
ρ resistivity ohm metre Ω⋅m kg⋅m3⋅s−3⋅A−2
P electric power watt W = V⋅A kg⋅m2⋅s−3
C capacitance farad F = C/V kg−1⋅m−2⋅A2⋅s4
ΦE electric flux volt metre V⋅m kg⋅m3⋅s−3⋅A−1
E electric field strength volt per metre V/m = N/C kg⋅m⋅A−1⋅s−3
D electric displacement field coulomb per square metre C/m2 A⋅s⋅m−2
ε permittivity farad per metre F/m kg−1⋅m−3⋅A2⋅s4
χe electric susceptibility (dimensionless) 1 1
p electric dipole moment coulomb metre C⋅m A⋅s⋅m
G; Y; B conductance; admittance; susceptance siemens S = Ω−1 kg−1⋅m−2⋅s3⋅A2
κ, γ, σ conductivity siemens per metre S/m kg−1⋅m−3⋅s3⋅A2
B magnetic flux density, magnetic induction tesla T = Wb/m2 = N⋅A−1⋅m−1 kg⋅s−2⋅A−1
Φ, ΦM, ΦB magnetic flux weber Wb = V⋅s kg⋅m2⋅s−2⋅A−1
H magnetic field strength ampere per metre A/m A⋅m−1
F magnetomotive force ampere A = Wb/H A
R magnetic reluctance inverse henry H−1 = A/Wb kg−1⋅m−2⋅s2⋅A2
P magnetic permeance henry H = Wb/A kg⋅m2⋅s–2⋅A–2
L, M inductance henry H = Wb/A = V⋅s/A kg⋅m2⋅s−2⋅A−2
μ permeability henry per metre H/m kg⋅m⋅s−2⋅A−2
χ magnetic susceptibility (dimensionless) 1 1
m magnetic dipole moment ampere square meter A⋅m2 = J⋅T−1 A⋅m2
σ mass magnetization ampere square meter per kilogram A⋅m2/kg A⋅m2⋅kg−1

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, "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.[35]

Applications

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The study of electromagnetism informs electric circuits, magnetic circuits, and semiconductor devices' construction.

See also

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References

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Further reading

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Electromagnetism

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Electromagnetism is a fundamental branch of physics that describes the interactions between electric charges and magnetic fields, unifying electricity and magnetism as aspects of a single force that governs the behavior of charged particles and subatomic entities. This force, one of the four fundamental interactions of nature and described by the Standard Model of particle physics, operates through electric and magnetic fields generated by accelerating or moving charges, with photons as the mediating particles that propagate its effects over infinite distances, though weakening with distance. Key principles include the attraction between opposite charges and repulsion between like charges, as well as the induction of magnetic fields by moving electric charges and electric fields by changing magnetic fields, forming a reciprocal relationship encapsulated in . These equations—comprising Gauss's law for electricity, Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's addition—mathematically describe how electric fields (E) and magnetic fields (B) interact, revealing that varying fields self-propagate as electromagnetic waves at the speed of light. Unlike mechanical waves, electromagnetic waves require no medium and travel through the vacuum of space, manifesting as light, radio waves, and other forms of radiation essential to communication, energy transfer, and observation of the universe. Electromagnetism underpins atomic structure by binding electrons to nuclei, drives chemical reactions and biological processes, and enables technologies from power generation to telecommunications. Its relativistic interpretation shows magnetic effects as consequences of electric forces observed from moving frames, highlighting the theory's consistency with special relativity.

History

Ancient and Early Observations

Early observations of magnetic phenomena date back to ancient China, where texts from the 4th century BCE, such as the Guiguzi, describe the attractive properties of lodestone (magnetite). By around 200 BCE, during the Han Dynasty, the Chinese employed lodestone in spoon-shaped devices known as "south-pointers" for divination purposes, marking an early practical application of magnetism's directional qualities. These devices, though not initially used for navigation, demonstrated an understanding of lodestone's ability to align with the Earth's magnetic field, laying foundational knowledge for later compass development. In ancient Greece, philosophers in the 6th century BCE, particularly Thales of Miletus (c. 624–546 BCE), documented both magnetic attraction and static electricity. Thales observed that lodestone naturally attracts iron, attributing it to an animistic "soul" within the material, and noted that amber, when rubbed with wool or fur, generates an attractive force capable of drawing light objects like feathers or straw. These qualitative descriptions represented some of the earliest recorded distinctions between magnetic and electric effects, though they remained philosophical rather than experimental. Ancient Egyptian medical practices around 2500 BCE incorporated electric fish, such as the Nile catfish (Malapterurus electricus), for therapeutic purposes, as evidenced by tomb reliefs depicting their use in treating pain and inflammation. This early form of electrotherapy involved applying the fish's electric discharges to alleviate ailments like headaches and gout, predating written records but confirmed through archaeological iconography. Similar knowledge of bioelectric phenomena appears in other ancient civilizations, highlighting a widespread recognition of natural electrical effects for healing. In the late 16th century, English physician William Gilbert advanced these ideas through his seminal 1600 treatise De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet, Magnetic Bodies, and the Great Magnet of the Earth). Gilbert systematically distinguished electricity—produced by frictional charging of materials like amber—from true magnetism, which he observed only in iron and lodestone. He coined the term "electric" (from the Greek ēlektron for amber) to describe substances capable of frictional attraction and proposed that the Earth itself functions as a giant magnet, explaining compass behavior through experiments with spherical "terrella" models. Building on Gilbert's work, German engineer Otto von Guericke conducted early experiments with frictional electricity in the 1650s, inventing the first electrostatic generator: a rotating sulfur globe rubbed to produce visible sparks and attract light objects. Guericke's device, demonstrated publicly and described in his 1672 correspondence with Gottfried Leibniz, allowed for stronger and more consistent electrical effects than manual rubbing, paving the way for quantitative studies in the following century.

19th Century Developments

In 1785, Charles-Augustin de Coulomb conducted precise experiments using a torsion balance to measure the attractive and repulsive forces between charged objects, demonstrating that the electric force follows an inverse-square law proportional to the product of the charges and inversely proportional to the square of the distance between them. This quantitative law provided a foundational empirical basis for electrostatics, building on earlier qualitative observations of electric phenomena. The pivotal link between electricity and magnetism emerged in 1820 when Hans Christian Ørsted observed that an electric current passing through a wire caused a nearby compass needle to deflect, indicating that moving charges produce magnetic fields. Ørsted's serendipitous discovery during a lecture demonstration revealed the intimate connection between the two forces, overturning the prevailing view of their independence and sparking rapid advancements in the field. Inspired by Ørsted's finding, André-Marie Ampère quickly developed a mathematical theory in the early 1820s, formulating the force law between two parallel current-carrying wires as proportional to the product of the currents and inversely proportional to the square of their separation. Through meticulous experiments with wires, solenoids, and electromagnets, Ampère established that magnetic forces arise from electric currents, introducing concepts like the ampere unit and laying the groundwork for electrodynamics. Michael Faraday advanced this unification in 1831 with his experiments on electromagnetic induction, showing that a changing magnetic field induces an electric current in a nearby conductor, as demonstrated by moving a magnet near a coil or varying current in one circuit to affect another. Faraday's iron ring apparatus, which produced the first induced current, led to the invention of the primitive electric generator—a rotating copper disk between magnet poles that generated continuous current—enabling practical applications of electromagnetic principles. His qualitative laws of induction emphasized field lines and flux changes, avoiding mathematical formalism at the time. Independently, American physicist Joseph Henry conducted similar induction experiments in the early 1830s, constructing efficient electromagnets and discovering self-induction, where a changing current in a coil induces a back electromotive force. Henry's innovations included the electromagnetic relay in 1835, a device using a weak induced current to control a stronger one, which amplified signals over long distances and became essential for early telegraphy. His work, often overlooked due to limited publications, paralleled Faraday's and contributed to high-intensity motors and practical electromagnetic devices. The theoretical culmination came with James Clerk Maxwell's work from 1861 to 1865, where he synthesized Coulomb's, Ampère's, and Faraday's contributions into a set of four differential equations describing the interrelations of electric and magnetic fields. In his 1865 paper "A Dynamical Theory of the Electromagnetic Field," Maxwell introduced the displacement current term to Ampère's law, predicting that varying electric fields generate magnetic fields and vice versa, leading to the propagation of electromagnetic waves at the speed of light and unifying electricity, magnetism, and optics. This framework established electromagnetism as a coherent field theory, with light as an electromagnetic disturbance. Experimental validation arrived in 1887 when Heinrich Hertz generated and detected electromagnetic waves using a spark-gap transmitter and loop receiver, confirming their transverse nature, reflection, refraction, and polarization as predicted by Maxwell. Hertz's apparatus produced waves with wavelengths of about 1 to 10 meters, demonstrating propagation through space without wires and providing empirical proof of the wave theory of light. His findings paved the way for radio technology and solidified the 19th-century unification of electromagnetic phenomena.

20th Century Advances

In the late 19th century, Hendrik Lorentz formulated the force law describing the motion of charged particles in electromagnetic fields, which became foundational for understanding relativistic effects. This Lorentz force law, developed in the 1890s, played a pivotal role in Albert Einstein's 1905 theory of special relativity, where electromagnetic phenomena revealed the equivalence of mass and energy, encapsulated in the relation E=mc2E = mc^2, demonstrating that electromagnetic energy contributes to inertial mass. Building on James Clerk Maxwell's unification of electricity, magnetism, and light in the 1860s, these advances integrated electromagnetism with spacetime geometry, enabling predictions of phenomena like electromagnetic mass in accelerating charges. The early 20th century saw the emergence of quantum electrodynamics (QED) as the quantum field theory of electromagnetism, addressing inconsistencies in classical theory at atomic scales. Paul Dirac's 1928 relativistic quantum equation for electrons incorporated electromagnetic interactions but encountered infinities in higher-order calculations. In the 1940s, Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga independently developed renormalization techniques to resolve these divergences, yielding finite, predictive results for electromagnetic processes like electron-photon scattering. Their work, honored by the 1965 Nobel Prize in Physics, established QED as the most precisely tested theory in physics, with predictions matching experiments to parts per billion. World War II accelerated practical applications of electromagnetism through microwave technology, originating from radar developments in the 1940s. British and American scientists, including those at MIT's Radiation Laboratory, advanced centimeter-wave radar systems using magnetrons, enabling detection of aircraft and ships over long distances. This wartime innovation laid the groundwork for post-war microwave communications, powering satellite relays, cellular networks, and wireless broadcasting by the 1950s and beyond. The 1960s marked the invention of the laser, harnessing stimulated emission within electromagnetic fields to produce coherent light. Theoretical foundations from the 1950s by Charles Townes and Arthur Schawlow, building on Einstein's 1917 prediction of stimulated emission, culminated in Theodore Maiman's 1960 demonstration of the first ruby laser. This device amplified light via population inversion in a resonant cavity, revolutionizing fields from optics to medicine through precise, high-intensity electromagnetic beams.

21st Century Advances

In the 21st century, Hans G. Schantz developed an energy-velocity framework for classical electromagnetism, building on 's 1893 derivation of electromagnetic energy velocity. This approach describes reactive near fields based on the local speed of energy transport rather than proximity to the source. The framework introduces the "Great Electromagnetic Circle," a parametric mapping of energy balance states that aids in the mathematical analysis of phenomena such as radiation reaction paradoxes and wave interference. Published in Philosophical Transactions of the Royal Society A in 2018, the model has received a modest number of citations (approximately 10-20 for the 2018 paper as per historical data, though current figures may vary slightly) and has fueled practical applications—including numerous patented inventions (approximately 25-30) in ultra-wideband antennas and near-field wireless systems that enhance efficiency in communications and positioning technologies. Electromagnetism has driven breakthroughs in ultrafast and quantum materials research. The 2016 Nobel Prize in Physics awarded to David Thouless, Duncan Haldane, and Michael Kosterlitz highlighted topological phases in quantum materials, including topological insulators where surface electrons behave as massless Dirac fermions under electromagnetic fields, promising dissipationless electronics. Similarly, the 2023 Nobel Prize in Physics recognized Pierre Agostini, Ferenc Krausz, and Anne L'Huillier for generating attosecond pulses of light—electromagnetic waves lasting 10−1810^{-18} seconds—via high-harmonic generation in gases, allowing real-time observation of electron dynamics in atoms and molecules. Experimental verifications continue to affirm QED's electromagnetic predictions with extraordinary precision. The Fermilab Muon g-2 experiment's 2021 measurement of the muon's anomalous magnetic moment strengthened evidence for a discrepancy with Standard Model predictions to 4.2 sigma significance, with a precision of 0.20 parts per million. The 2025 final result, with 0.127 parts per million precision, combined with updated theoretical calculations (particularly lattice QCD contributions to hadronic vacuum polarization), resolved this tension, confirming agreement with QED to within uncertainties as of November 2025 and affirming the Standard Model without evidence for new physics.

Fundamental Nature

The Electromagnetic Force

The electromagnetic force is one of the four fundamental interactions of nature, governing the interactions between electrically charged particles. Classically, it encompasses both electric and magnetic forces, which were unified in the 19th century, with the linkage between electricity and magnetism first demonstrated experimentally by Hans Christian Ørsted in 1820 when he observed a compass needle deflecting near a current-carrying wire. In the quantum description provided by quantum electrodynamics, the force is mediated by the exchange of virtual photons between charged particles, enabling both attractive and repulsive effects depending on the charges involved. This force is extraordinarily strong compared to gravity, being approximately 103610^{36} times more powerful at the scale of elementary particles, though its effects largely cancel out in electrically neutral matter composed of equal numbers of positive and negative charges. Relative to the other fundamental forces, electromagnetism is about 10410^4 times stronger than the weak nuclear force, which operates on subatomic scales to mediate processes like beta decay, but it is weaker than the strong nuclear force by a factor of roughly 100 at the distances within atomic nuclei. These relative strengths highlight electromagnetism's dominance in phenomena involving charged particles outside of nuclear interiors. The electromagnetic force is essential to the structure of atoms, where it attracts negatively charged electrons to the positively charged nucleus, determining atomic radii and stability, while repulsion between electrons prevents collapse and shapes electron orbitals. This same force underpins chemistry by facilitating the attraction and repulsion that form chemical bonds, such as covalent and ionic bonds in molecules, enabling the vast diversity of chemical reactions and materials observed in nature. Unlike the short-range strong nuclear force, which is confined to about 10−1510^{-15} meters, the electromagnetic force has infinite range, with its strength diminishing according to an inverse-square law, F∝1/r2F \propto 1/r^2, allowing it to influence particles across cosmic distances. Its manifestations are ubiquitous in everyday physics, including the repulsion or attraction between static charges, the magnetic fields generated by electric currents in wires, the persistent magnetism in materials like iron due to aligned atomic-scale currents, and electromagnetic radiation such as visible light and radio waves that propagate energy through space.

Unification with Other Forces

The electroweak unification, proposed in the 1960s, merges electromagnetism with the weak nuclear force into a single framework based on the SU(2)×U(1)SU(2) \times U(1) gauge symmetry group. Sheldon Glashow introduced the foundational idea in 1961 with a model featuring intermediate vector bosons for weak interactions and a mixing angle to relate electromagnetic and weak couplings. Independently, Steven Weinberg in 1967 and Abdus Salam in 1968 developed the full theory, incorporating spontaneous symmetry breaking via the Higgs mechanism to generate masses for the W and Z bosons while keeping the photon massless. This Glashow-Weinberg-Salam (GWS) model predicted neutral weak currents and the existence of heavy W± and Z bosons, with the electromagnetic interaction emerging as the low-energy limit after electroweak symmetry breaking. For their contributions, Glashow, Weinberg, and Salam shared the 1979 Nobel Prize in Physics. The theory's predictions were experimentally confirmed by the discovery of the W and Z bosons at CERN in 1983, with masses around 80 and 91 GeV, respectively, aligning closely with GWS calculations. Within the Standard Model of particle physics, electromagnetism arises as the unbroken U(1)U(1) subgroup of the electroweak gauge group after symmetry breaking at the electroweak scale of approximately 246 GeV. The photon mediates the electromagnetic force, while the massive W and Z bosons handle charged and neutral weak interactions, respectively. This unification resolves long-standing issues in weak interaction phenomenology, such as parity violation, and provides a renormalizable quantum field theory describing all electroweak processes with high precision, tested in experiments like those at LEP and the LHC. Efforts to further unify electromagnetism with the strong nuclear force led to grand unified theories (GUTs) in the 1970s. The seminal SU(5) model by Howard Georgi and Sheldon Glashow in 1974 embeds the Standard Model gauge group SU(3)C×SU(2)L×U(1)YSU(3)_C \times SU(2)_L \times U(1)_Y into a single SU(5)SU(5) group at an energy scale around 101610^{16} GeV, predicting that quarks and leptons reside in unified multiplets and that the three gauge couplings converge. A key testable prediction is baryon number violation, manifesting as proton decay, such as p→e++π0p \to e^+ + \pi^0, with an estimated lifetime of about 103110^{31} years in minimal SU(5). However, no proton decay has been observed; experiments like Super-Kamiokande have set lower limits on the lifetime exceeding 103410^{34} years for this mode, constraining or ruling out minimal SU(5) without extensions like supersymmetry. String theory, developed prominently from the 1980s onward, proposes a more comprehensive unification by treating fundamental particles as vibrational modes of one-dimensional strings in 10 spacetime dimensions (or 11 in M-theory). The electromagnetic force emerges from specific string excitations and compactified extra dimensions, alongside the other forces and gravity, within a consistent quantum framework that avoids ultraviolet divergences plaguing point-particle theories. The first superstring revolution in 1984, driven by anomaly cancellation in heterotic strings, solidified this approach as a candidate for embedding all interactions, including electromagnetism, in higher-dimensional geometry. Despite these advances, significant challenges persist in unifying electromagnetism with other forces. The hierarchy problem highlights the vast disparity between the electroweak scale (∼102\sim 10^2 GeV) and the GUT scale (∼1016\sim 10^{16} GeV), requiring unnatural fine-tuning to keep the Higgs mass light against quantum corrections from high-scale physics. Moreover, incorporating gravity remains elusive in GUTs, as general relativity resists quantization in flat-space field theories; string theory addresses this by unifying gravity naturally but struggles with the lack of direct experimental tests and the landscape of possible vacua, complicating unique predictions for low-energy electromagnetism.

Classical Theory

Electrostatics and Magnetostatics

Electrostatics describes the behavior of electric charges at rest and the stationary electric fields they produce. The fundamental law governing the interaction between two point charges is Coulomb's law, which states that the electrostatic force F\mathbf{F} between two point charges q1q_1 and q2q_2 separated by a distance rr is given by F=kq1q2r2r^,\mathbf{F} = k \frac{q_1 q_2}{r^2} \hat{\mathbf{r}}, where k=14πϵ0k = \frac{1}{4\pi\epsilon_0} is Coulomb's constant, ϵ0\epsilon_0 is the vacuum permittivity with value 8.854×10−12 F⋅m−18.854 \times 10^{-12} \, \mathrm{F \cdot m^{-1}}, and r^\hat{\mathbf{r}} is the unit vector from one charge to the other. This law, experimentally established by Charles-Augustin de Coulomb using a torsion balance in 1785, indicates that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them, and it acts along the line joining the charges. To analyze the effects of multiple charges, the concept of the electric field E\mathbf{E} is introduced, defined as the force F\mathbf{F} per unit positive test charge qq at a point in space: E=Fq.\mathbf{E} = \frac{\mathbf{F}}{q}. The electric field due to a point charge QQ at distance rr is thus E=14πϵ0Qr2r^\mathbf{E} = \frac{1}{4\pi\epsilon_0} \frac{Q}{r^2} \hat{\mathbf{r}}. Electric field lines provide a visual representation, originating from positive charges and terminating on negative charges, with their density indicating field strength; the lines are perpendicular to equipotential surfaces and follow the direction of force on a positive test charge. A key integral theorem for electrostatics is Gauss's law, which relates the electric flux through a closed surface to the enclosed charge: ∮E⋅dA=Qenclϵ0.\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\mathrm{encl}}}{\epsilon_0}. This law, formulated by Carl Friedrich Gauss and published posthumously in 1867, is particularly useful for symmetric charge distributions, such as spheres or cylinders, allowing the calculation of E\mathbf{E} without direct integration of Coulomb's law. It underscores the conservative nature of electrostatic fields, where the curl of E\mathbf{E} is zero, implying the field can be derived from a scalar potential ϕ\phi via E=−∇ϕ\mathbf{E} = -\nabla \phi. Magnetostatics addresses the magnetic fields produced by steady currents, independent of time-varying electric fields. The Biot-Savart law gives the infinitesimal magnetic field dBd\mathbf{B} at a point due to a small current element IdlI d\mathbf{l}: dB=μ04πIdl×r^r2,d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \hat{\mathbf{r}}}{r^2}, where μ0=4π×10−7 N⋅A−2\mu_0 = 4\pi \times 10^{-7} \, \mathrm{N \cdot A^{-2}} is the vacuum permeability, and the cross product ensures B\mathbf{B} is perpendicular to both the current direction and the position vector r\mathbf{r}. This law was derived experimentally by Jean-Baptiste Biot and Félix Savart in 1820 through measurements of magnetic forces on compass needles near current-carrying wires. For a closed loop or infinite straight wire, integrating the Biot-Savart law yields specific field configurations, such as the circumferential field around a wire. Ampère's law provides an integral form for magnetostatics, stating that the line integral of B\mathbf{B} around a closed path equals μ0\mu_0 times the enclosed current: ∮B⋅dl=μ0Iencl.\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\mathrm{encl}}. Formulated by André-Marie Ampère in the 1820s following Oersted's discovery of electromagnetism, this law is analogous to Gauss's law and simplifies calculations for symmetric current distributions, like solenoids or toroids. It implies that magnetic fields are divergenceless (∇⋅B=0\nabla \cdot \mathbf{B} = 0), with no magnetic monopoles, and can be expressed via a vector potential A\mathbf{A} as B=∇×A\mathbf{B} = \nabla \times \mathbf{A}. In magnetic materials, the relationship between B\mathbf{B}, the magnetic field H\mathbf{H}, and material magnetization M\mathbf{M} is B=μ0(H+M)\mathbf{B} = \mu_0 (\mathbf{H} + \mathbf{M}), often approximated as B=μH\mathbf{B} = \mu \mathbf{H} where μ=μ0μr\mu = \mu_0 \mu_r and μr\mu_r is the relative permeability. Diamagnetic materials, such as bismuth and copper, exhibit weak repulsion from magnetic fields due to induced opposing currents, with μr<1\mu_r < 1 (e.g., μr≈0.99999\mu_r \approx 0.99999 for water). Paramagnetic materials, like aluminum and oxygen, are weakly attracted, with 1<μr<21 < \mu_r < 2, as atomic magnetic moments align partially with the applied field. Ferromagnetic materials, including iron and nickel, show strong attraction and hysteresis, with μr\mu_r up to thousands, due to aligned electron spins forming domains; they retain magnetization after field removal, enabling permanent magnets. The Lorentz force law unifies electrostatic and magnetostatic effects on a charged particle, giving the total force as F=q(E+v×B),\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}), where qq is the charge and v\mathbf{v} its velocity. Derived by Hendrik Lorentz in 1895, this expression shows the electric force qEq\mathbf{E} acts directly on the charge, while the magnetic force qv×Bq \mathbf{v} \times \mathbf{B} depends on motion and is always perpendicular to v\mathbf{v}, doing no work. In static fields, this force governs particle trajectories in devices like cyclotrons, without inducing field changes.

Electromagnetic Induction and Waves

Electromagnetic induction refers to the generation of an electromotive force (EMF) in a conductor due to a changing magnetic field. In 1831, Michael Faraday discovered this phenomenon through experiments involving coils and magnets, demonstrating that a time-varying magnetic flux through a circuit induces an electric current. The quantitative formulation, known as Faraday's law, states that the induced EMF ϵ\epsilon in a closed loop is equal to the negative rate of change of magnetic flux ΦB\Phi_B through the surface bounded by the loop: ϵ=−dΦBdt,\epsilon = -\frac{d\Phi_B}{dt}, where ΦB=∫B⋅dA\Phi_B = \int \mathbf{B} \cdot d\mathbf{A}. , formulated by Heinrich Lenz in 1834, specifies the direction of the induced current, stating that it creates a magnetic field opposing the change in flux that produced it. This principle ensures conservation of energy, as the induced current's opposition requires work against the changing field. For instance, when a magnet approaches a conducting loop, the induced current generates a field repelling the magnet. Inductance quantifies the ability of a circuit to store energy in its magnetic field and oppose changes in current. Self-inductance LL for a single coil is defined as the ratio of the magnetic flux linkage to the current: L=Φ/IL = \Phi / I, with units of henry (H). Mutual inductance MM between two coils arises when current in one produces flux through the other, given by M=Φ21/I1M = \Phi_{21} / I_1, where Φ21\Phi_{21} is the flux through coil 2 due to current I1I_1 in coil 1. Transformers exploit mutual inductance to transfer energy between circuits, stepping up or down AC voltage via coupled coils on a magnetic core, with the voltage ratio approximately equal to the turns ratio. A key extension to induction came from James Clerk Maxwell's 1861 introduction of displacement current, which addressed inconsistencies in Ampère's law for time-varying fields. Maxwell added the term ϵ0∂E/∂t\epsilon_0 \partial \mathbf{E}/\partial t to the conduction current density in Ampère's circuital law, representing the rate of change of electric flux in regions without conduction current, such as between capacitor plates. This modification, ∇×B=μ0J+μ0ϵ0∂E/∂t\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \partial \mathbf{E}/\partial t, ensures continuity of current and enables symmetric treatment of electric and magnetic fields. The inclusion of displacement current allows derivation of the electromagnetic wave equation from Maxwell's equations. Taking the curl of Faraday's law (∇×E=−∂B/∂t\nabla \times \mathbf{E} = -\partial \mathbf{B}/\partial t) and substituting into the modified Ampère's law (and vice versa) in vacuum yields the wave equation for the electric field: ∇2E=1c2∂2E∂t2,\nabla^2 \mathbf{E} = \frac{1}{c^2} \frac{\partial^2 \mathbf{E}}{\partial t^2}, where the speed c=1/μ0ϵ0≈3×108c = 1/\sqrt{\mu_0 \epsilon_0} \approx 3 \times 10^8
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