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Topic: A Dynamical Theory of the Electromagnetic Field

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Maxwells equations

Lorentz equation

Unified field theory

A Treatise on Electricity and Magnetism

Gauge transformation

Electromagnetism

Displacement current

James Clerk Maxwell

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	NationMaster - Encyclopedia: Hendrik Lorentz
		Electromagnetic radiation or EM radiation is a combination (cross product) of oscillating electric and magnetic fields perpendicular to each other, moving through space as a wave, effectively transporting energy and momentum.
		During the first twenty years in Leiden Lorentz was primarily interested in the theory of electromagnetism, to explain the relationship of electricity, magnetism, and light.
		These mathematical formulas describe basic effects of the theory of Special relativity, namely the increase of mass, shortening of length, and time dilation that are characteristic of a moving body, all of which Lorentz had discussed in his 1899 publication.
	www.nationmaster.com /encyclopedia/Hendrik-Lorentz (7426 words)

	Unified field theory - Wikipedia, the free encyclopedia
		In physics, unified field theory is an attempt to unify all the fundamental forces and the interactions between elementary particles into a single theoretical framework.
		This unified theory was governed by the exchange of four particles: the photon for electromagnetic interactions, and a neutral Z particle and two charged W particles for weak interaction.
		Their theory was given experimental support by the discovery, in 1983, of the Z and W bosons at CERN by Carlo Rubbia's team.
	en.wikipedia.org /wiki/Unified_field_theory (1426 words)

	Maxwell's equations - Wikipedia, the free encyclopedia
		The electromagnetic field equations have an intimate link with special relativity: the magnetic field equations can be derived from consideration of the transformation of the electric field equations under relativistic transformations at low velocities.
		Einstein motivated the special theory by noting that a description of a conductor moving with respect to a magnet must generate a consistent set of fields irrespective of whether the frame is the magnet frame or the conductor frame..
		This equation is related to the magnetic field's structure because it states that given any volume element, the net magnitude of the vector components that point outward from the surface must be equal to the net magnitude of the vector components that point inward.
	en.wikipedia.org /wiki/Maxwell's_equations (3534 words)

	The Need For a New Model of the Earth The Living and Dynamic Earth
		The Dynamics Explorer, a space probe used to study the solar wind's interaction with the Earth and the mechanisms behind the formation of the aurora, also uncovered evidence that does not support the present model, but is expected of this new model.
		The Field near Gibraltar, at the mouth of the Mediterranean, is referred to as the Mediterranean Field.
		During winter the South Polar Field is activated as a Field that releases ionizing radiation, and it is this that is heating the troposphere.
	www.livingcosmos.com /earth.htm (12423 words)

	List of Publications by Iwo Bialynicki-Birula
		Field theory of photon dust, Acta Physica Polonica B 23, 553 (1992).
		Nonstandard introduction to squeezing of the electromagnetic field, Acta Phys.
		Squeezing of electromagnetic field in a cavity by electrons in Trojan states (with P. Kochanski and Z. Bialynicka-Birula), Phys.
	www.cft.edu.pl /~birula/publ.html (2428 words)

	The Invention of Knowledge - A Theory of Knowledge
		Since a theory of knowledge is unfamiliar, it may be instructive to look at what a great theory in the discipline of physics is like; and Maxwell's theory of the Electromagnetic Field is the most beautiful example I know.
		But the field is three-dimensional and fortunately by the 19th century the Calculus was extended to rates of change in three dimensions using double and triple integrals and partial differentials.
		Our theory of knowledge, if it is powerful, should extend to other parts of knowledge that were not included in the development of the theory and provide us with some wonderful surprises.
	www.artifacts.com /10theoryofknow.html (3119 words)

	Faraday and Maxwell (Site not responding. Last check: 2007-10-11)
		The specific features of Faraday's field concept, in its 'favourite' and most complete form, are that force is a substance, that it is the only substance and that all forces are interconvertible through various motions of the lines of force.
		The incorporation of optics into the theory of electromagnetism, with its relation of the speed of light to the electric and magnetic absolute system of units as well as the relation of the refraction coëfficient and the metallic conductivity of the body—it was like a revelation.
		A modern commemorative reprint of A Dynamical Theory of the Electromagnetic Field with prefatory and introductory comments by Thomas Torrance, editor, and an appreciation of Maxwell's influence by Albert Einstein was published by Wipf and Stock Publishers, Eugene, Oregon, 1982.
	www.cox-internet.com /hermital/book/holoprt4-3.htm (1333 words)

	Sketching the History of Classical Electromagnetism (Site not responding. Last check: 2007-10-11)
		The partial-drag theory of George Gabriel Stokes (1819-1903) is revived for the explanation of stellar aberration.
		Maxwell's A Dynamical Theory of the Electromagnetic Field, formulating an electrodynamical formulation of wave propagation using Lagrangian and Hamiltonian techniques, obtaining the theoretical possibility of generating electromagnetic radiation.
		Oliver Heaviside (1850-1925) writes Electromagnetic induction and its propagation over the course of two years, re-expressing Maxwell's results in 3 (complex) vector form, giving it much of its modern form and collecting together the basic set of equations from which electromagnetic theory may be derived (often called "Maxwell's equations").
	history.hyperjeff.net /electromagnetism.html (2851 words)

	The Electromagnetic Field & Clerk Maxwell - Albert Einstein [1931]
		Secondly, the nature of the electromagnetic field itself is the closest specification that man has made in relation to the nature of light - the medium of his highest physical sense - that of vision.
		This relates to the fact that although his equations expressed the mathematical properties of the energy intrinsic to the continuous field of space and time, he was unable to reconcile in a satisfactory manner, the ways in which the two basic forms of this energy, in respect of position and motion, manifest themselves.
		By the turn of the century the conception of the electromagnetic field as an irreducible entity was already generally established and serious theorists had given up confidence in the justification, or the possibility, of a mechanical foundation for Maxwell's equations.
	www.mountainman.com.au /aether_2.html (2383 words)

	Myswizard » Unified Field Theory and The Theory of Everything
		The primary problem in producing a TOE is that the accepted theories of quantum mechanics and general relativity propose radically different descriptions of the universe, and straightforward ways of combining the two lead quickly to the renormalization problem in which the theory does not give finite results for experimentally testable quantities.
		There has been progress toward a TOE in unifying electromagnetism and the weak nuclear force in an electroweak unified field theory and in unifying all of the forces except for gravity (which in the present theory of general relativity is not a force) in the grand unification theory.
		The theory argues that current scientific theory is inconsistent and incomplete in that it predicts yet doesn’t explain Action at a distance, violates its own conservation laws, and fails to live up to experimental data or concur with the laws of common sense.
	www.myswizard.com /2006/01/31/unified-field-theory-and-the-theory-of-everything (3117 words)

	Altair Explains Electromagnetics
		This electromagnetic force is what gives material objects the illusion of solidity even though they are composed of 99.999% empty space.
		The latent force of electromagnetism may be mathematically described by a field of vectors, hence the term force field.
		Electromagnetic radiation has a dual nature, this duality means sometimes we see the wave-nature and sometimes we see the particle-nature.
	www.altair.org /emag.html (916 words)

	The Tom Bearden Website
		His general equations of the electromagnetic field are given in Part III, General Equations of the Electromagnetic Field, p.
		Also, in 1967 Ludwig Lorenz developed a parallel theory of electrodynamics very similar to Maxwell's, and he also symmetrically regauged his equations (which is a dramatic simplification, indeed one which arbitrarily discards any net interaction between an active environment and the physical system being modeled).
		And that, together with Faraday's notion that his field lines were physical, like taut strings in space, meant that perturbation of the "field lines" in space gave a set of "plucked string" or transverse wave oscillations.
	www.cheniere.org /correspondence/050402.htm (1480 words)

	M Theory Visionists - Refraction of Light
		His proposal of this wave theory of light was not accepted by most English scientists of the period because it opposed Newton's theory of light.
		According to this last theory space is filled with an extremely rare ether, and light is caused by a series of waves or vibrations in this ether which are set in motion by the pulsations of the luminous body.
		The quantum field theory approach visualizes the force between the electeons as an exchange force arising from the exchange of virtual photons.
	worldcrossing.com /WebX?128@@.1ddee4cd (5569 words)

	Footprints (Site not responding. Last check: 2007-10-11)
		In the last decade of the 18th century, intrigued by the electrostatic experiments of Joseph Priestly (1733-1804), Charles-Augustin de Coulomb (1736-1806) formulated the mathematics of the Coulomb force and the inverse square law as it applies to electrostatics and magnetostatics.
		This classic essay, Maxwell's second on electromagnetism, was based on the latest contemporary scientific knowledge available at that time and served as the foundation for early studies of the electromagnetic field.
		Maxwell also notes that the electromagnetic theory of light developed in his Dynamical Theory of the Electromagnetic Field essay "is the same in substance" as that which Faraday presented in his 1846 essay, Thoughts on Ray Vibrations.
	www.cox-internet.com /hermital/book/holoprt2-3.htm (1380 words)

	Ether and the Theory of Relativity
		This theory also called the theory of the stationary luminiferous ether moreover found a strong support in an experiment which is also of fundamental importance in the special theory of relativity, the experiment of Fizeau, from which one was obliged to infer that the luminiferous ether does not take part in the movements of bodies.
		The electromagnetic fields are not states of a medium, and are not bound down to any bearer, but they are independent realities which are not reducible to anything else, exactly like the atoms of ponderable matter.
		According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration.
	www.tu-harburg.de /rzt/rzt/it/Ether.html (2930 words)

	James Clerk Maxwell: A Treatise on Electricity and Magnetism
		Maxwell expressed electromagnetism in the algebra of quaternions and made the electromagnetic potential the centerpiece of his theory.
		As examples, since the time when the theoretical design of electromagnetism was frozen, gauge theory has been invented and brought to maturity and topology and geometry have been introduced to field theory.
		The EM field in massless space is force-free, and is a "condition of space" itself, as pointed out by Feynman in his three volumes of sophomore physics.
	www.rexresearch.com /maxwell.htm (1994 words)

	Explaining Earth's Magnetic Field and Oceanic Magnetic Banding
		Mathematical derivation of the strength of the resultant quadrupole field is rather involved, and it is dependent on a large number of variables, including the spacing between the centers of the two convection cells.
		The empirical field strengths and orientations and the anomalies and drift of the Earth's Magnetic Field are extremely complex.
		Again, the (net) total field measured at the surface of the Earth is the sum of the magnetic fields of many such pseudo-randomly oriented convection cells (or symmetric cell pairs), so that the total net measured effect could fluctuate erratically and quickly.
	mb-soft.com /public/tecto2.html (6881 words)

	Newman's Theory: A Report
		He came to the conclusion that if electromagnetic fields consisted of tiny spinning particles moving at the speed of light along the field lines, then he could explain all standard electromagnetic phenomena through the interaction of spinning particles.
		Given that electromagnetic fields consist of matter in motion, or kinetic energy, Joe decided that it should be possible to tap this kinetic energy.
		An electrical field would require one second to travel the length of the wire, or in Newman's language, it would take one second for gyrotons inserted at one end of the wire to reach the other end.
	www.padrak.com /ine/NEWMAN3.html (2532 words)

	Physics College of Engineering - University of Massachusetts Dartmouth
		Also examined are Maxwells equations, momentum and energy of the electromagnetic field, radiation, multipole expansions, scattering, special relativity and Lagrangian formulation, radiation from moving charge, radiation reaction.
		Study of simple radiating systems, scattering and diffraction of electromagnetic waves, radiation by moving charges, special theory of relativity, Lorentz transformation, covariant formulation of Maxwells equations, relativistic particle dynamics, scattering of charged particles, radiation damping and self-fields of a charged particle.
		Relativistic kinematics of particle motion, phenomenological and dynamical theories of particle interactions and classification of particles according to symmetry principles.
	www.umassd.edu /engineering/phy/courses/lvl_600.cfm (835 words)

	On Maxwell and Maxwellian views of charge and current
		Although Maxwell's model of the field provided a way to understand electromagnetic phenomena from a mechanical point of view, his mathematical structure of the field survived the late nineteenth century rejection of the mechanistic world view (in favor of electrodynamics) and became the basis of later elaborations developed by Heinrich Hertz and others.
		Maxwellian theory has one deep feature that distinguishes it from electromagnetism after the electron: Maxwellian theory assumes that applying Hamilton's principle to suitably chosen field energy densities (with appropriate medium constants) is all that is necessary to obtain satisfactory mathematical expressions of electromagnetic phenomena.
		In modern electromagnetic theory, charge is the source of electric fields, and current is the source of the magnetic fields.
	www.victorianweb.org /science/maxwell.html (943 words)

	ULB - ONT: Teaching Activities
		The basis of the nonlinear optics developed in these notes is the electromagnetic theory of Maxwell which is a difficult theory to understand because the field is a unifying but abstract concept.
		Maxwell's formulation of the laws of electromagnetism is the first example of a unified field theory.
		The major difficulty with this theory is that although the field equations are linear, which makes them conceptually simple, measurable quantities such as energy, intensity, power,...
	www.ulb.ac.be /sciences/ont/EnTeach.html (457 words)

	General relativity
		General relativity is a theory of gravitation and to understand the background to the theory we have to look at how theories of gravitation developed.
		In 1907, two years after proposing the special theory of relativity, Einstein was preparing a review of special relativity when he suddenly wondered how Newtonian gravitation would have to be modified to fit in with special relativity.
		Einstein applied his theory of gravitation and discovered that the advance of 43" per century was exactly accounted for without any need to postulate invisible moons or any other special hypothesis.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/General_relativity.html (1995 words)

	[No title]
		Supergravity [PHYS] A supersymmetry which is used to unify general relativity and quantum theory; it is formed by adding to the poincare group, as a symmetry of space-time, four new generators that behave as spinors and vary as the square root of the translations.
		Patent numbers 5,473,957 and 5,150,626 describe implementations of super- conducting magnetic fields of the quadrupole electromagnetic configuration and the equivalence principle that illustrates the effects of an acceleration field being equal to the effects of a gravitational field.
		The development of a theory of gravitation based on the exchange of gravitons and the unification of this theory with the GUT (Grand Unified field Theory) is the task that this generation of inventors like Mr.
	www.supersymmetry.com (2345 words)

	The Hindu : Education Plus Coimbatore : Einstein and a century of Physics
		All of classical physics at the fundamental level could be summarised by two great systems of dynamical laws, one was due to Newton and governed `Matter' and the other was due to Maxwell and governed `Field', the electromagnetic field.
		Maxwell's dynamical laws for the electromagnetic field were based on the intuitive picture of the electric and magnetic fields that Faraday had built out of the results of many famous experiments.
		Once Maxwell succeeded in constructing his complete and consistent system of mathematical equations dictating the dynamical behaviour of the electromagnetic field, he could predict that electromagnetic waves existed and that their speed would be 300,000 km per second.
	www.hindu.com /edu/2005/02/14/stories/2005021407230400.htm (943 words)

	The Field Equations
		Thus, guided by the belief that the laws of physics should be the simplest possible tensor equations (to ensure general covariance), he proposes that the field equations for the gravitational field in empty space should be
		A slight (but significant) extension of the field equations was proposed by Einstein in 1917 based on cosmological considerations, as a means of ensuring stability of a static closed universe.
		In his original 1916 paper on the general theory Einstein initially selected coordinates such that the metric determinant g was a constant -1, in which case the partial derivatives of
	www.mathpages.com /rr/s5-08/5-08.htm (1713 words)

	[No title]
		During this time, the Maxwell theory had not really made very much progress, and though considered of importance, it was not considered anything very spectacular -- much of this being because of its "considered too difficult" mathematics and the residues of the "terrible quaternions".
		Today, in modern quantum theory we know that it is the potentials that have the primary reality, and the force fields are merely constructed from them (by their interaction in and with charged matter).
		The result is to equalize the back emf (translation force field that must be opposed by all current pumped back through the generator) and the forward emf (translation force field that pushes the current to flow through the external circuit and thus enables powering the external circuit's loads and losses.
	www.cheniere.org /correspondence/030706.htm (3633 words)

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