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Topic: Electromagnetic tensor

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curvature tensor

tensor field

tensor algebra

tensor product of fields

Classical treatment of tensors

Tensor intrinsic definition

Tensor product of R algebras

Intermediate treatment of tensors

Component free treatment of tensors

Ricci tensor

rank of a tensor

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	- electromagnetic processes in dispersive media: a treatment based on the dielectric tensor by d. b. melrose, isbn ...
		Electromagnetic Processes in Dispersive Media: A Treatment Based on the Dielectric Tensor by D. Melrose, ISBN 0521410258
		This text presents a systematic discussion of electromagnetic waves and radiation processes in a wide variety of media.
		The treatment, taken from the field of plasma physics, is based on the dielectric tensor; the authors unify approaches used in plasma physics and astrophysics on the one hand and in optics on the other.
	www.yourplasmatvspace.com /Electromagnetic-Processes-in-Dispersive-Media:-A-Treatment-Based-on-the-Dielectric-Tensor-by-D.-B.-Melrose,-ISBN-0521410258/Content/2226735 (1266 words)

	Tensors
		Tensors are used in various parts of physics, both as abstract constructs in mathematical physics and for describing relations between quantities represented by matrices.
		Diffusion tensor imaging (DTI) is a method for imaging the fibrous structure of organs in the body, such as the brain, using the diffusivity of water.
		The electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor or Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field of a physical system in Maxwell's theory of electromagnetism.
	www.shortopedia.com /T/E/Tensors (848 words)

	A Symetric Derivation of the Electromagnetic Energy-Momentum Tensor (Site not responding. Last check: 2007-10-26)
		A symmetric derivation of the of the energy-momentum tensor for the electromagnetic field is presented, by treating the interaction between the field and both electric and magnetic charges on equal footing.
		That the specification of the divergence of an antisymmetric tensor and the divergence of it's dual completely determines the tensor (and hence in this case, the fields) is a generalization of Helmholtz's theorem to four dimensional space time [8], the divergence of the dual playing the role of the curl.
		A frequent approach to defining the energy-momentum tensor for the electromagnetic field is to generalize the definition of the Hamiltonian density to a covariant form[9].
	vortex.brynmawr.edu /vortex/eppaper.html (1488 words)

	Electromagnetic tensor - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-26)
		The field tensor was first used after the 4-dimensional tensor formulation of special relativity introduced by Hermann Minkowski.
		Hidden beneath the surface of this complex mathematical equation is an ingenious unification of Maxwell's equations for electromagnetism.
		The field tensor derives its name from the fact that the electromagnetic field is found to obey the tensor transformation law, this general property of (non-gravitational) physical laws being recognised after the advent special relativity.
	en.wikipedia.org /wiki/Electromagnetic_field_tensor (784 words)

	Tensor Electromagnetic Profiling of the San Andreas fault Martyn Unsworth and John Booker, P.I.'s Dept. of Earth and ...
		Tensor Electromagnetic Profiling of the San Andreas fault Martyn Unsworth and John Booker, P.I.'s Dept. of Earth and Space Sciences, University of Washington
		Tensor Electromagnetic Profiling of the San Andreas fault 1434-94-6-2423 - Martyn Unsworth and John Booker, P.I.'s Dept.
		The model was derived by inversion of tensor magnetotelluric and is the smoothest model that fits the data.
	www.pnsn.org /REPTS/mt.html (1370 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		The second sacrifice is the ambiguity of determining of an electromagnetic field tensor and it appreciably impedes using of the tensor for practical calculations.
		The third sacrifice is the difficulty to associate the tensor with real physical object and/or process, or else, physical sense fails to be found for an electromagnetic field tensor.
		It is interesting to mark, that the presence of the imaginary components of the tensor is conditioned by necessity to obtain negative components in a quadratic form, i.e.
	www.pwaves.0catch.com /doc/english/e57.htm (288 words)

	Electromagnetic Field -- from Eric Weisstein's World of Physics
		The electric and magnetic components of an electromagnetic field are untitled in special relativity into an entity known as the electromagnetic field tensor.
		The potential energy of an electromagnetic field consisting of an electric field E and a magnetic field B in cgs is
		For a particle in an electromagnetic field, the motion is circular.
	scienceworld.wolfram.com /physics/ElectromagneticField.html (178 words)

	ELECTROMAGNETIC - THE PHOTON - POLARITONS IN PERIODIC AND QUASIPERIODIC STRUCTURES - REBECCA OF SUNNYBROOK FARM (DVD)
		This anthology of primary readings chronicles the birth and maturation of five such theories (the heliocentric theory, the electromagnetic field theory, special and general relativity, quantum theory, and the big bang theory) in the words of the scientists who brought them to life.
		It is the first historical account that captures the rich substance of these theories, each of which represents a fascinating story of the interplay of evidence and insight--and of dialogue among great minds.
		Over the last decade, enormous progress in the understanding of T-cell homing has made it possible to identify the multitude of molecules involved, such as cytokines, chemokines, and adhesion molecules, and to unravel their complex interactions resulting in controlled, non-random T-cell recirculation.
	www.yourelectromagneticspace.com /The_Photon/Articles/2515511 (1378 words)

	PHYS 457 - Electromagnetic Theory II (Site not responding. Last check: 2007-10-26)
		Tensor formulation of Maxwell's equations and the Lorentz force equation.
		A thorough discussion of the relativistic tensor formalism is given only in PHYS 501.
		The Lorentz transformation properties of the electric and magnetic fields should be discussed, and the magnetic field accompanying an electric current should be explained as a result of applying a Lorentz transformation to the static electric field present in the frame that is comoving with the current.
	www.phas.ucalgary.ca /phasweb/courses/undergrad/457.php (248 words)

	Maxwell's equations Modern Relativity modernrelativity special general black hole mass energy Einstein wormhole time ...
		The electromagnetic tensor in local Cartesian coordinates is Eqn.
		Show that the covariant duel of the contravariant duel of the a covarient antisymmetric tensor of rank two is the original tensor times -1.
		In this case, the local inertial frame observes a gravitational field that is not zero a finite extent away from the charged particle.
	www.geocities.com /zcphysicsms/chap7.htm (1155 words)

	Subject outline information for
		The subject is intended to introduce classical electromagnetic theory embodying Maxwell's equations with applications mainly to situations where electric charge can be treated as a continuous fluid.
		Examination questions will be set on the fundamental components of classical electromagnetic theory as outlined in lectures and examination problems will be of the type solved in tutorial classes.
		Tensor notation, dual vector spaces, the role of tensors in the formulation of relativistic theories.
	www.physics.uq.edu.au /people/jones/ph348/profile/PHYS3050.html (573 words)

	The summaries you suggested I prepare (Site not responding. Last check: 2007-10-26)
		Further, it is found that the current density coupled to the electromagnetic field strength tensor, is directly related to the gradient of E dot B. E dot B is thus integrally and inextricably linked to sources, both gravitational and electrodynamic.
		However, because the perfect fluid tensor with diag{mu, p, p, p} has an eigenvalue p with multiplicity either 3 or 4 and the electromagnetic tensor has two distinct eigenvalues, each with multiplicity 2, and although some of the equations (5.1) do not vanish, the Poynting vector does vanish everywhere.
		By injecting electrons into an electromagnetic field and recording their movement under tightly controlled circumstances where the only difference from one run to the next entails a controlled difference in temperature or pressure, slight variations in the path of movement may be observed.
	www.lns.cornell.edu /spr/2006-04/msg0073710.html (763 words)

	EM Green's tensor library for horizontally layered anisotropic mediumn (Site not responding. Last check: 2007-10-26)
		We describe the arbitrary piecewise-uniform distribution of material property functions along the z direction and assume that in the chosen coordinate system these tensor functions in principal axes are transverse isotropic (Figure 1).
		The EM Green's tensors represent elementary electrical and magnetic fields excited by the point electrical and magnetic dipoles.
		Cheryauka, A.,B., and M.S. Zhdanov, 2001, Electromagnetic tensor Green's functions in a transverse isotropic layered medium, IEEE Transactions on Geosciences and Remote Sensing (Submitted).
	www.mines.utah.edu /~wmcemi/appls/bhole/gt3d/gt3d.html (361 words)

	Electromagnetic Field Gauges
		A few are well known: the Coulomb gauge for classical electromagnetism, the Lorenz gauge which makes electromagnetism look like a simple harmonic oscillator, and the gauge invariant form which is used in the Maxwell equations.
		The anti-symmetric 2-rank electromagnetic field tensor F has 3 properties: its trace is zero, it is antisymmetric, and it contains all the components of the E and B fields.
		The field tensor F in the temporal gauge is quite similar to the Coulomb gauge, but some of the signs have changed to target the dphi/dt term.
	www.theworld.com /~sweetser/quaternions/EandM/gauges/gauges.html (513 words)

	ModPhy/Unit1/SpecialRelativity/InvariantView/Tensors/
		Tensors are physical quantities resulting from the sum of the ordered product of two or more vectors.
		Similarly, setting the exterior derivative of the 4D electromagnetic field tensor equal to zero gives two of Maxwell’s electromagnetic field equations and setting the divergence of this 4-D tensor equal to the 4-D current density vector renders Maxwell’s other two field equations.
		Electromagnetic Tensor –.The four-dimensional anti-symmetrical electromagnetic field tensor.
	physics.tamuk.edu /~hewett/ModPhy1/Unit1/SpecialRelativity/InvariantView/Tensors/Tensors.html (362 words)

	How does matter couple to space-time so that space-time becomes curved?
		The components of the Riemann tensor identically satisfy a differential equation (the Bianchi identity), which is why the metric tensor (ten algebraically independent components at each event) can and does completely determine the Riemann curvature tensor (20 algebraically independent components at each event).
		The Weyl tensor turns out to be analogous in many ways to the electromagnetic field tensor, which you can think of as an antisymmetric four by four matrix (6 algebraically independent components at each event).
		Another important way in which the gravitational field is analogous to the electromagnetic field is that, just as small disturbances in the electromagnetic field at a given even propagate outward as an electromagnetic wave, so too small disturbances in the the gravitational field at a given event propagate outward as a gravitational wave.
	www.physlink.com /Education/AskExperts/ae98.cfm (689 words)

	GRTensorII demonstrations-General Relativity & Geometry. (Site not responding. Last check: 2007-10-26)
		Demonstration 1 (ss1): The Einstein tensor and Kretschmann scalar are calculated for the spherically symmetric self-similar metric in curvature coordinates.
		Demonstration 2 (ss2): The Einstein tensor and Kretschmann scalar are calculated for the spherically symmetric self-similar metric in comoving coordinates.
		Demonstration 3 (ss3): The Einstein tensor and Kretschmann scalar are calculated for the spherically symmetric self-similar metric in Bondi coordinates.
	grtensor.phy.queensu.ca /NewDemo/demo.html (1569 words)

	EM History
		The third area of research in electromagnetic theory in the late nineteenth and twentieth centuries was the compilation of mathematical analysis techniques to solve Maxwell’s equations in a variety of configurations.
		For example, to calculate the electromagnetic waves scattering from an object, one could model the object as a sphere and then express the electromagnetic field as a mathematical function that satisfies Maxwell’s equations in all space as well as the correct boundary conditions for Maxwell’s equations at the surface of the sphere.
		Galvani’s lasting contribution to the science of electromagnetics was to excite the interest of contemporary Italian scientist Alessandro Volta, who found the correct explanation for the source of electric current in the absence of a mechanical generator.
	users.wsg.net /bedrosian/em_history.htm (16327 words)

	PX421 Relativity and Electrodynamics
		The main aim is to develop your appreciation of the unification of electrical and magnetic effects in the electromagnetic field under special relativity.
		Energy in electromagnetism, Poynting's theorem and conservation of energy, momentum density, radiation pressure, Maxwell stress tensor, source of radiation pressure for a conductor, conservation of linear and angular momentum in electromagnetic fields.
		Transformation of electromagnetic fields by extension of the Galilean transformation, experimental evidence for the Lorentz invariance of charge, four-current density.
	www2.warwick.ac.uk /fac/sci/physics/teach/syllabi/year4/px421 (477 words)

	CEMI Software (Site not responding. Last check: 2007-10-26)
		Electromagnetic modeling of a three-dimensional structure embedded in a multi-layer anisotropic earth, using integral equations approach.
		Electromagnetic Matlab is an unified software package for EM and potential fields modeling and inversion based on the Matlab Language of Technical Computing.
		It generates a linear equation with respect to the modified conductivity tensor which is proportional to the reflectivity tensor and the complex anomalous conductivity.
	www.mines.utah.edu /~wmcemi/soft/index.html (6142 words)

	[No title]
		Further, the so-called filtered Green's tensor, which increases the application range of the coupled-dipole approximation to higher permittivity scatterers can also be computed [1].
		Analytical expressions from the free space Green's tensor are combined to obtain the electrostatic Green's tensor associated with a surface.
		For the filtered Green's tensor, a spectral approach, with integration in complex space is used [2,3].
	www.cpc.cs.qub.ac.uk /summaries/ADPS_v1_0.html (190 words)

	My Grand Unified Field Theory (Site not responding. Last check: 2007-10-26)
		The manner of the rotation is the same as described by the electromagnetic tensor.
		Electromagnetic acceleration is acceleration caused by the electromagnetic force.
		Unlike gravitational acceleration, which is irrespective of the mass-energy of the affected object, acceleration caused by electromagnetism is inversely proportional to the mass-energy of the affected object.
	lofi.forum.physorg.com /My-Grand-Unified-Field-Theory_6711.html (8252 words)

	The Stress Tensor of the Electromagnetic Field (Site not responding. Last check: 2007-10-26)
		A tensor is a bookkeeping device designed to keep together elements that transform in a similar way.
		Together, the energy density(W), Poynting's vector (Sa) and the Maxwell stress tensor (m_ab) are all the components of the stress tensor of the electromagnetic field.
		The rest of that tensor is generated by the second line.
	world.std.com /~sweetser/quaternions/EandM/tensor/tensor.html (614 words)

	New Transformation Equations and the Electric Field Four-vector
		The electric field is described by a four-vector and the electromagnetic field tensor is replaced by the electric field tensor.
		In this theory, unlike in relativity, we use a Euclidean metric to describe spacetime, leading to a redefinition of the invariance of the speed of light and the propagation of light in four dimensions rather than three.
		The equations (12.2) are analogous to Maxwell's electromagnetic field equations.
	www.softcom.net /users/der555/full.html (3920 words)

	New Transformation Equations and the Electric Field Four-vector
		These terms are responsible for the appearance of additional terms in many of the existing laws of physics, for example, Maxwell's electromagnetic field equations, the Lorentz four-force equations, and the electromagnetic energy-momentum tensor.
		In rectangular coordinates, the derivative of a tensor is identical to the ordinary derivative.
		Because of this, all ordinary derivatives of tensors must be replaced by their covariant derivatives.
	www.softcom.net /users/der555/node22.html (3756 words)

	Tools of Tensor calculus - An overview
		In this section we shall analyze the electromagnetic field produced by a charge moving with uniform velocity v with respect to an observer.
		As you can see, the output for tensors expanded in the natural basis are very close to the handwritten notation.
		The metric tensor in terms of the null tetrad is easily obtained performing a basis change in
	baldufa.upc.es /xjaen/ttc/tutorial/tour.htm (1149 words)

	PHY2214 Classical Theory of Fields
		For vectors, dyadics etc. to be truly invariant under a set of coordinate transformations their components must transform in very specific ways, i.e., must be components of tensors of the appropriate rank.
		In this sense it may be said that the mathematics of tensor analysis and tensor calculus is truly the language of physics.
		It also shows how the dynamics of these fields (such as Einstein's laws of relativistic dynamics and Maxwell's equations of electromagnetism) can be obtained by constructing maximally simple Lorentz-invariant action functionals with subsequent application of a universal principle (the principle of least action).
	newton.ex.ac.uk /teaching/modules/PHY2214.html (438 words)

	Physics 302 (Site not responding. Last check: 2007-10-26)
		The definition of the dual of the electromagnetic tensor.
		The divergence of the stress-energy tensor as a restatement of conservation of energy and momentum.
		An alternative expression for the EM stress-energy tensor that avoids the dual of the electromagnetic tensor.
	www.sdss.jhu.edu /~ethan/302.html (575 words)

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