Electromagnetism is a branch of 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 fields composed of electric fields and magnetic fields, is responsible for electromagnetic radiation such as light, and is one of the four fundamental interactions (commonly called forces) in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation.[1] At high energy the weak force and electromagnetic force are unified as a single electroweak force.

Lightning is an electrostatic discharge that travels between two charged regions.

Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force, which includes both electricity and 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 and their orbital electrons holds atoms together. Electromagnetic forces are responsible for the chemical bonds between atoms which create molecules, and intermolecular forces. The electromagnetic force governs all chemical processes, which arise from interactions between the electrons of neighboring atoms.

There are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential and electric current. In Faraday's law, magnetic fields are associated with electromagnetic induction and magnetism, and Maxwell's equations 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), led to the development of special relativity by Albert Einstein in 1905.

History of the theory

Originally, electricity and magnetism were considered to be two separate forces. This view changed, however, with the publication of James Clerk Maxwell's 1873 A Treatise on Electricity and Magnetism 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: unlike charges attract, like ones repel.
  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.
  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.
  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.

While preparing for an evening lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. As he was setting up his materials, he noticed a compass needle deflected away from magnetic north when the electric current from the battery he was using was switched on and off. This deflection convinced him that magnetic fields radiate from all sides of a wire carrying an electric current, just as light and heat do, and that it confirmed a direct relationship between electricity and magnetism.

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 unit of magnetic induction (oersted) is named in honor of his contributions to the field of electromagnetism.

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.[2] 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, 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.[3]

An earlier (1735), and often neglected, connection between electricity and magnetism was reported by a Dr. Cookson.[4] 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." [5]

Fundamental forces

Circular.Polarization.Circularly.Polarized.Light Right.Handed.Animation.305x190.255Colors
Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation.

The electromagnetic force is one of the four known fundamental forces. The other fundamental forces are:

All other forces (e.g., friction, contact forces) are derived from these four fundamental forces (including momentum which is carried by the movement of particles).[6]

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 atoms can be explained by the electromagnetic force acting between the electrically charged atomic nuclei and electrons 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 forces that act between the individual molecules in our bodies and those in the objects. The electromagnetic force is also involved in all forms of 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 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.[7]

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. 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. One of the first to discover and publish a link between man-made electric current and magnetism was 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.[8] 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, was developed by various physicists during the period between 1820 and 1873 when it culminated in the publication of a treatise by James Clerk Maxwell, which unified the preceding developments into a single theory and discovered the electromagnetic nature of light.[9] 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.[10]

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 a 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.)

Extension to nonlinear phenomena

Sun in X-Ray
Magnetic reconnection in the solar plasma gives rise to solar flares, a complex magnetohydrodynamical phenomenon.

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. This is studied, for example, in the subject of magnetohydrodynamics, which combines Maxwell theory with the Navier–Stokes equations.

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:

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. 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[11] Name of quantity Unit name Symbol Base units
Q electric charge coulomb C A⋅s
I electric current ampere A A (= W/V = C/s)
J electric current density ampere per square metre A/m2 A⋅m−2
U, ΔV, Δφ; E potential difference; 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
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 = kg⋅s−2⋅A−1 = N⋅A−1⋅m−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
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

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.

See also


  1. ^ Ravaioli, Fawwaz T. Ulaby, Eric Michielssen, Umberto (2010). Fundamentals of applied electromagnetics (6th ed.). Boston: Prentice Hall. p. 13. ISBN 978-0-13-213931-1.
  2. ^ Darrigol, Olivier (2000). Electrodynamics from Ampère to Einstein. New York: Oxford University Press. ISBN 0198505949.
  3. ^ Martins, Roberto de Andrade. "Romagnosi and Volta's Pile: Early Difficulties in the Interpretation of Voltaic Electricity" (PDF). In Fabio Bevilacqua and Lucio Fregonese (eds) (eds.). Nuova Voltiana: Studies on Volta and his Times. vol. 3. Università degli Studi di Pavia. pp. 81–102. Archived from the original (PDF) on 2013-05-30. Retrieved 2010-12-02.CS1 maint: Uses editors parameter (link)
  4. ^ VIII. An account of an extraordinary effect of lightning in communicating magnetism. Communicated by Pierce Dod, M.D. F.R.S. from Dr. Cookson of Wakefield in Yorkshire. Phil. Trans. 1735 39, 74-75, published 1 January 1735
  5. ^ Whittaker, E.T. (1910). A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century. Longmans, Green and Company.
  6. ^ Browne, "Physics for Engineering and Science," p. 160: "Gravity is one of the fundamental forces of nature. The other forces such as friction, tension, and the normal force are derived from the electric force, another of the fundamental forces. Gravity is a rather weak force... The electric force between two protons is much stronger than the gravitational force between them."
  7. ^ Purcell, "Electricity and Magnetism, 3rd Edition," p. 546: Ch 11 Section 6, "Electron Spin and Magnetic Moment."
  8. ^ Stern, Dr. David P.; Peredo, Mauricio (2001-11-25). "Magnetic Fields – History". NASA Goddard Space Flight Center. Retrieved 2009-11-27.
  9. ^ Purcell, p. 436. Chapter 9.3, "Maxwell's description of the electromagnetic field was essentially complete."
  10. ^ Purcell: p. 278: Chapter 6.1, "Definition of the Magnetic Field." Lorentz force and force equation.
  11. ^ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. pp. 14–15. Electronic version.

Further reading

Web sources


  • G.A.G. Bennet (1974). Electricity and Modern Physics (2nd ed.). Edward Arnold (UK). ISBN 978-0-7131-2459-0.
  • Browne, Michael (2008). Physics for Engineering and Science (2nd ed.). McGraw-Hill/Schaum. ISBN 978-0-07-161399-6.
  • Dibner, Bern (2012). Oersted and the discovery of electromagnetism. Literary Licensing, LLC. ISBN 978-1-258-33555-7.
  • Durney, Carl H.; Johnson, Curtis C. (1969). Introduction to modern electromagnetics. McGraw-Hil]. ISBN 978-0-07-018388-9.
  • Feynman, Richard P. (1970). The Feynman Lectures on Physics Vol II. Addison Wesley Longman. ISBN 978-0-201-02115-8.
  • Fleisch, Daniel (2008). A Student's Guide to Maxwell's Equations. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-70147-1.
  • I.S. Grant; W.R. Phillips; Manchester Physics (2008). Electromagnetism (2nd ed.). John Wiley & Sons. ISBN 978-0-471-92712-9.
  • Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 978-0-13-805326-0.
  • Jackson, John D. (1998). Classical Electrodynamics (3rd ed.). Wiley. ISBN 978-0-471-30932-1.
  • Moliton, André (2007). Basic electromagnetism and materials. 430 pages. New York City: Springer-Verlag New York, LLC. ISBN 978-0-387-30284-3.
  • Purcell, Edward M. (1985). Electricity and Magnetism Berkeley, Physics Course Volume 2 (2nd ed.). McGraw-Hill. ISBN 978-0-07-004908-6.
  • Purcell, Edward M and Morin, David. (2013). Electricity and Magnetism, 820p (3rd ed.). Cambridge University Press, New York. ISBN 978-1-107-01402-2.CS1 maint: Multiple names: authors list (link)
  • Rao, Nannapaneni N. (1994). Elements of engineering electromagnetics (4th ed.). Prentice Hall. ISBN 978-0-13-948746-0.
  • Rothwell, Edward J.; Cloud, Michael J. (2001). Electromagnetics. CRC Press. ISBN 978-0-8493-1397-4.
  • Tipler, Paul (1998). Physics for Scientists and Engineers: Vol. 2: Light, Electricity and Magnetism (4th ed.). W.H. Freeman. ISBN 978-1-57259-492-0.
  • Wangsness, Roald K.; Cloud, Michael J. (1986). Electromagnetic Fields (2nd Edition). Wiley. ISBN 978-0-471-81186-2.

General references

  • A. Beiser (1987). Concepts of Modern Physics (4th ed.). McGraw-Hill (International). ISBN 978-0-07-100144-1.
  • L.H. Greenberg (1978). Physics with Modern Applications. Holt-Saunders International W.B. Saunders and Co. ISBN 978-0-7216-4247-5.
  • R.G. Lerner; G.L. Trigg (2005). Encyclopaedia of Physics (2nd ed.). VHC Publishers, Hans Warlimont, Springer. pp. 12–13. ISBN 978-0-07-025734-4.
  • J.B. Marion; W.F. Hornyak (1984). Principles of Physics. Holt-Saunders International Saunders College. ISBN 978-4-8337-0195-2.
  • H.J. Pain (1983). The Physics of Vibrations and Waves (3rd ed.). John Wiley & Sons. ISBN 978-0-471-90182-2.
  • C.B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. ISBN 978-0-07-051400-3.
  • R. Penrose (2007). The Road to Reality. Vintage books. ISBN 978-0-679-77631-4.
  • P.A. Tipler; G. Mosca (2008). Physics for Scientists and Engineers: With Modern Physics (6th ed.). W.H. Freeman and Co. ISBN 978-1-4292-0265-7.
  • P.M. Whelan; M.J. Hodgeson (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN 978-0-7195-3382-2.

External links

Biot–Savart law

In physics, specifically electromagnetism, the Biot–Savart Law ( or ) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot–Savart law is fundamental to magnetostatics, playing a role similar to that of Coulomb's law in electrostatics. When magnetostatics does not apply, the Biot–Savart law should be replaced by Jefimenko's equations. The law is valid in the magnetostatic approximation, and is consistent with both Ampère's circuital law and Gauss's law for magnetism. It is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820.

Charge (physics)

In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by the letter Q, and so the invariance of the charge corresponds to the vanishing commutator , where H is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues q of the generator Q.

Charged particle

In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary particle, which are all believed to have the same charge (except antimatter). Another charged particle may be an atomic nucleus devoid of electrons, such as an alpha particle.

A plasma is a collection of charged particles, atomic nuclei and separated electrons, but can also be a gas containing a significant proportion of charged particles.

Classical electromagnetism

Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics.

Fundamental physical aspects of classical electrodynamics are presented in many texts, such as those by Feynman, Leighton and Sands, Griffiths, Panofsky and Phillips, and Jackson.

Covariant formulation of classical electromagnetism

The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. These expressions both make it simple to prove that the laws of classical electromagnetism take the same form in any inertial coordinate system, and also provide a way to translate the fields and forces from one frame to another. However, this is not as general as Maxwell's equations in curved spacetime or non-rectilinear coordinate systems.

This article uses the classical treatment of tensors and Einstein summation convention throughout and the Minkowski metric has the form diag (+1, −1, −1, −1). Where the equations are specified as holding in a vacuum, one could instead regard them as the formulation of Maxwell's equations in terms of total charge and current.

For a more general overview of the relationships between classical electromagnetism and special relativity, including various conceptual implications of this picture, see Classical electromagnetism and special relativity.

Dark radiation

Dark radiation (also dark electromagnetism) is a postulated type of radiation that mediates interactions of dark matter.

By analogy to the way photons mediate electromagnetic interactions between particles in the Standard Model (called baryonic matter in cosmology), dark radiation is proposed to mediate interactions between dark matter particles. Similar to dark matter particles, the hypothetical dark radiation does not interact with Standard Model particles.

There has been no notable evidence for the existence of such radiation, but since baryonic matter contains multiple interacting particle types, it is reasonable to suppose that dark matter does also. Moreover, it has been pointed out recently that the cosmic microwave background data seems to suggest that the number of effective neutrino degrees of freedom is more than 3.046, which is slightly more than the standard case for 3 types of neutrino. This extra degree of freedom could arise from having a non-trivial amount of dark radiation in the universe. One possible candidate for dark radiation is the sterile neutrino.

Electric field

An electric field surrounds an electric charge, and exerts force on other charges in the field, attracting or repelling them. Electric field is sometimes abbreviated as E-field. The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The SI unit for electric field strength is volt per meter (V/m). Newtons per coulomb (N/C) is also used as a unit of electric field strength. Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature.

Electric power

Electric power is the rate, per unit time, at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

Electric power is usually produced by electric generators, but can also be supplied by sources such as electric batteries. It is usually supplied to businesses and homes (as domestic mains electricity) by the electric power industry through an electric power grid. Electric energy is usually sold by the kilowatt hour (1 kW·h = 3.6 MJ) which is the product of the power in kilowatts multiplied by running time in hours. Electric utilities measure power using an electricity meter, which keeps a running total of the electric energy delivered to a customer.

Electrical power provides a low entropy form of energy and can be carried long distances and converted into other forms of energy such as motion, light or heat with high energy efficiency.

Electromagnetic field

An electromagnetic field (also EMF or EM field) is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction).

The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law. The force created by the electric field is much stronger than the force created by the magnetic field.From a classical perspective in the history of electromagnetism, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles.

Electromagnetic tensor

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely.


Electrophoresis (from the Greek "Ηλεκτροφόρηση" meaning "to bear electrons") is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. Electrophoresis of positively charged particles (cations) is sometimes called cataphoresis, while electrophoresis of negatively charged particles (anions) is sometimes called anaphoresis.

The electrokinetic phenomenon of electrophoresis was observed for the first time in 1807 by Russian professors Peter Ivanovich Strakhov and Ferdinand Frederic Reuss at Moscow State University, who noticed that the application of a constant electric field caused clay particles dispersed in water to migrate. It is ultimately caused by the presence of a charged interface between the particle surface and the surrounding fluid. It is the basis for analytical techniques used in chemistry for separating molecules by size, charge, or binding affinity.

Electrophoresis is used in laboratories to separate macromolecules based on size. The technique applies a negative charge so proteins move towards a positive charge. Electrophoresis is used extensively in DNA, RNA and protein analysis.


Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. A flux is either a concept based in physics or used with applied mathematics. Both concepts have mathematical rigor, enabling comparison of the underlying mathematics when the terminology is unclear. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In electromagnetism, flux is a scalar quantity, defined as the surface integral of the component of a vector field perpendicular to the surface at each point.


In special and general relativity, the four-current (technically the four-current density) is the four-dimensional analogue of the electric current density. Also known as vector current, it is used in the geometric context of four-dimensional spacetime, rather than three-dimensional space and time separately. Mathematically it is a four-vector, and is Lorentz covariant.

Analogously, it is possible to have any form of "current density", meaning the flow of a quantity per unit time per unit area. see current density for more on this quantity.

This article uses the summation convention for indices. See covariance and contravariance of vectors for background on raised and lowered indices, and raising and lowering indices on how to switch between them.

Jefimenko's equations

In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay (retarded time) of the fields due to the finite speed of light and relativistic effects. Therefore they can be used for moving charges and currents. They are the general solutions to Maxwell's equations for any arbitrary distribution of charges and currents.

Maxwell's equations

Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (c) in the vacuum, the "speed of light". Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations that included the Lorentz force law. He also first used the equations to propose that light is an electromagnetic phenomenon.

The equations have two major variants. The microscopic Maxwell equations have universal applicability, but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the atomic scale. The "macroscopic" Maxwell equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale charges and quantum phenomena like spins. However, their use requires experimentally determined parameters for a phenomenological description of the electromagnetic response of materials.

The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the electric and magnetic potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics. The covariant formulation (on spacetime rather than space and time separately) makes the compatibility of Maxwell's equations with special relativity manifest. Maxwell's equations in curved spacetime, commonly used in high energy and gravitational physics, are compatible with general relativity. In fact, Einstein developed special and general relativity to accommodate the invariant speed of light, a consequence of Maxwell's equations, with the principle that only relative movement has physical consequences.

Since the mid-20th century, it has been understood that Maxwell's equations are not exact, but a classical limit of the fundamental theory of quantum electrodynamics.

Permeability (electromagnetism)

In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself, otherwise known as distributed inductance in Transmission Line Theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter µ. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.

In SI units, permeability is measured in henries per meter (H/m), or equivalently in newtons per ampere squared (N·A−2). The permeability constant µ0, also known as the magnetic constant or the permeability of free space, is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum. Until May 20, 2019, the magnetic constant had the exact (defined) value µ0 = 4π × 10−7 H/m ≈ 12.57 × 10−7 H/m.

On May 20, 2019 a revision to the SI system has gone into effect, making the vacuum permeability no longer a constant but rather a value that needs to be determined experimentally; 4π × 1.000 000 000 82 (20) 10−7 H·m−1 is a recently measured value in the new system. It will be proportional to the dimensionless fine-structure constant with no other dependencies.A closely related property of materials is magnetic susceptibility, which is a dimensionless proportionality factor that indicates the degree of magnetization of a material in response to an applied magnetic field.

Quark epoch

In physical cosmology the Quark epoch was the period in the evolution of the early universe when the fundamental interactions of gravitation, electromagnetism, the strong interaction and the weak interaction had taken their present forms, but the temperature of the universe was still too high to allow quarks to bind together to form hadrons. The quark epoch began approximately 10−12 seconds after the Big Bang, when the preceding electroweak epoch ended as the electroweak interaction separated into the weak interaction and electromagnetism. During the quark epoch the universe was filled with a dense, hot quark–gluon plasma, containing quarks, leptons and their antiparticles. Collisions between particles were too energetic to allow quarks to combine into mesons or baryons. The quark epoch ended when the universe was about 10−6 seconds old, when the average energy of particle interactions had fallen below the binding energy of hadrons. The following period, when quarks became confined within hadrons, is known as the hadron epoch.

Vacuum permittivity

The physical constant ε0 (pronounced as "epsilon nought" or "epsilon one"), commonly called the vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum. It has the value

ε0 = 8.8541878128(13)×10−12 F⋅m−1 (farads per metre).

It is the capability of the vacuum to permit electric field lines. This constant relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges (in the vacuum of classical electromagnetism) is given by Coulomb's law:

The value of the constant fraction is approximately 9 × 109 N⋅m2⋅C−2, q1 and q2 are the charges, and r is the distance between them. Likewise, ε0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources.


Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points (i.e., voltage) in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The official SI definition for volt uses power and current, where 1 volt = 1 watt (of power) per 1 ampere (of current). This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by ∆V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

Electric potential differences between points can be caused by electric charge, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage (or potential difference) between two points in a system; often a common reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy (electromotive force) or lost, used, or stored energy (potential drop).

Physical forces
Hypothetical forces
See also

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