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Encyclopedia > A Dynamical Theory of the Electromagnetic Field

A Dynamical Theory of the Electromagnetic Field was the third of James Clerk Maxwell's papers concerned with electromagnetism. The theory was the first paper in which Maxwell's equations appeared. The concept of displacement current was introduced, so that it became possible to derive equations of electromagnetic wave. James Clerk Maxwell (June 13, 1831–November 5, 1879) was a Scottish physicist, born in Edinburgh. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Piece of paper Paper is a thin, flat material produced by the compression of fibres. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... Displacement current is a pseudocurrent invented in 1865 by James Clerk Maxwell when formulating what are today known as Maxwells equations. ... Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ...

Contents


The original equations

In the original paper, because compact notations based on vectors had not yet been introduced, Maxwell formulated the equations in terms of 20 equations in 20 unknowns, as described in the Maxwell's equations article. Maxwell also included several equations now considered auxiliary to the core of Maxwell's equations. In physics and engineering, the word vector typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but this... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...


In modernized notation, the equations originally listed by Maxwell were:

Note that Maxwell did not consider completely general materials; his initial formulation used linear, isotropic, nondispersive permittivity ε and permeability μ, although he also discussed the possibility of anisotropic materials. The permittivity of a medium is an intensive physical quantity that describes how an electric field affects and is affected by the medium. ... Permeability has several meanings: In electromagnetism, permeability is the degree of magnetisation of a material in response to a magnetic field. ...


Here, is the magnetic field, which Maxwell called the "magnetic intensity". is the electric current density (with being the total current including displacement current). is the displacement field (called the "electric displacement" by Maxwell). ρ is the free charge density (called the "quantity of free electricity" by Maxwell). is the magnetic vector potential (called the "electromagnetic momentum" by Maxwell). is the electric field (called the "electromotive force" by Maxwell, not to be confused with the scalar quantity that is now called electromotive force). φ is the electric potential (which Maxwell also called "electric potential"). σ is the electrical conductivity (Maxwell called the inverse of conductivity the "specific resistance", what is now called the resistivity). Current flowing through a wire produces a magnetic field (M) around the wire. ... In vector calculus, a vector potential is a vector field which generates a solenoidal vector field. ... In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... Electromotive force (emf) is a measure of the strength of a source of electrical energy. ... Electric potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ... Electrical conductivity is a measure of how well a material accommodates the transport of electric charge. ... Electrical resistivity (also known as specific electrical resistance) is a measure indicating how strongly a material opposes the flow of electric current. ...


Note also that Maxwell further includes a term in his expression for the "electromotive force", which corresponds to the magnetic force per unit charge on a moving conductor with velocity . Due to this term, his expression was not strictly equal to the modern electric field except in the rest frame of the conductor. Velocity (symbol: v) is a vector measurement of the rate and direction of motion. ...


Quotes

This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws. Maxwell, Dynamical Theory of the Electromagnetic Field. 1865.
... we have strong reason to conclude that light itself -- including radiant heat, and other radiations if any -- is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws. Maxwell, Dynamical Theory of the Electromagnetic Field. 1864.

Cherenkov effect in a swimming pool nuclear reactor. ... 1865 is a common year starting on Sunday. ... Radiant energy is the energy transported by electromagnetic waves. ... 1864 was a leap year starting on Friday (see link for calendar). ...

See also

Timeline of electromagnetism and classical optics 130 — Claudius Ptolemy tabulates angles of refraction for several media, 1269 — Pélerin de Maricourt describes magnetic poles and remarks on the nonexistence of isolated magnetic poles, 1305 — Dietrich von Freiberg uses crystalline spheres and flasks filled with water to study the reflection and refraction...

Further reading

  • Maxwell, James Clerk, "A Dynamical Theory of the Electromagnetic Field", Philosophical Transactions of the Royal Society of London 155, 459-512 (1865). (This article accompanied a December 8, 1864 presentation by Maxwell to the Royal Society.)
  • Maxwell, James Clerk, "A Dynamical Theory of the Electromagnetic Field", Vol. CLV, 1865.
  • James C. Maxwell, Thomas F. Torrance, "A Dynamical Theory of the Electromagnetic Field". March, 1996. ISBN 1579100155
  • Niven, W. D., "The Scientific Papers of James Clerk Maxwell", 2 vols. Dover, New York, 1952, Vol. 1.

External links and references


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