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Topic: Magnetic vector potential

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Electric potential

	Magnetic Vector Potential (Site not responding. Last check: 2007-10-14)
		The vector potential is defined to be consistent with Ampere's Law and can be expressed in terms of either current i or current density j (the sources of magnetic field).
		One rationale for the vector potential is that it may be easier to calculate the vector potential than to calculate the magnetic field directly from a given source current geometry.
		Since the magnetic field B is defined as the curl of A, and the by vector identity the curl of a gradient is identically zero, then any arbitrary function which can be expressed as the gradient of a scalar function may be added to A without changing the value of B obtained from it.
	hyperphysics.phy-astr.gsu.edu /hbase/magnetic/magvec.html (235 words)

	Electric potential - Wikipedia, the free encyclopedia
		Electric potential is the potential energy per unit of charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts.
		This force has the same direction as the electric field vector, and its magnitude is given by the size of the charge multiplied with the magnitude of the electric field.
		The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential is mixed under Lorentz transformations.
	en.wikipedia.org /wiki/Electric_potential (1120 words)

	Magnetic potential - Wikipedia, the free encyclopedia
		There are two methods of relating the magnetic field to a potential field and they give rise to two possible types of magnetic potential.
		Conveniently, this solves the second of Maxwell's Equations automatically, which is to say that a continuous magnetic vector potential field is guaranteed not to result in magnetic monopoles.
		This may be done by joining a scalar electric potential with a vector magnetic potential or by joining a scalar magnetic potential with a vector electric potential.
	en.wikipedia.org /wiki/Magnetic_potential (556 words)

	(montalk.net) Research Notes: Magnetic Monopoles
		This means all the field lines of the vector potential curl into closed loops, and the magnetic force field points perpendicular to this curl.
		Really there is no such thing as magnetic field in itself, it is just that a magnetic particle released in a curled vector potential field will be forced to travel perpendicular to the curled parts of that field, and this bundle of forces we label a magnetic field.
		Divergence of the magnetic field is a mathematical quantity represented by `grad cdot bb B`.
	montalk.net /notes/magnetic-monopoles (366 words)

	Magnetic field: Vector potential (Site not responding. Last check: 2007-10-14)
		For the electric field the scalar electric potential provides both a convenient measurement and descriptive quantity (normalised potential energy) and a convenient calculating quantity.
		vector quantities, it is not possible to have a similar scalar quantity for the magnetic field.
		It is possible, however, to define a quantity, the magnetic vector potential, that often usefully simplifies the calculation of magnetic fields.
	www.physics.gla.ac.uk /~dland/ELMAG305/em10a/tsld023.htm (100 words)

	AVecWave
		A salient point is that the A vector is in the direction of the particle motion and is thus 90 degrees to the B field.
		The quantum electrogravitational potential is derived by integrating the vector magnetic potential A with respect to velocity in eq.
		The vector magnetic potential A cannot be shielded against as was demonstrated on a quantum scale by the famous Aharonhov-Bohm experiment involving electron diffraction patterns changing in a modified two-slit experiment in spite of the A field originating B field being absent.
	www.electrogravity.com /AVECWAVE (2228 words)

	A Formulation of the Problem
		The solution is often facilitated by defining potential functions in terms of the field vectors, because it is possible to transform the four first-order field equations to second-order equations in the potential functions that are formally integrable, if the boundary conditions are given.
		From the potential functions, it is possible to calculate E and B and the distributions of current densities and charge.
		From the symmetry of electric and magnetic field quantities, the second field equation (2.2) should be used for this purpose, since this is the electric analogue of the Maxwell's fourth equation (2.4).
	wheger.tripod.com /thesis/htm/th2.htm (2592 words)

	The Tom Bearden Website
		In potential theory, when the B-field (curl or swirl of the magnetic vector potential) is shielded and localized in that fashion, then in the space where the B-field would ordinarily be but now is not present, there appears a "field-free" and "swirl-free" or "curl-free" A-potential.
		ALMOST NONE of the magnetic B-field of the permanent magnet appears in the surrounding space; almost all of it is sucked into the core itself and held there.
		In that case, outside the core material there appears the curl-free magnetic vector potential A, because the local spacetime outside the core is still curved (which means it must contain excess energy) by the magnetic dipole.
	www.cheniere.org /correspondence/081602.htm (1376 words)

	Examples (Partial Differential Equation Toolbox)
		where B is the magnetic flux density, H is the magnetic field intensity, J is the current density, and µ is the material's magnetic permeability.
		Visualization of the magnetostatic potential A, the magnetic field H, and the magnetic flux density B is available.
		The magnetic permeability µ is 1 in the air and in the coil.
	www-rohan.sdsu.edu /doc/matlab/toolbox/pde/2examp17.html (837 words)

	Magnetic Flux (Site not responding. Last check: 2007-10-14)
		Magnetic flux is to charge as momentum is to mass.
		The words magnet and magnetism are derived from the Greek word "magnetite".
		Magnetite, a magnetic oxide of iron, was mined in Magnesia and mentioned in Greek texts as early as 800 BC.
	home.earthlink.net /~tdp/flux.html (276 words)

	EMAG: Chapter 1: Overview of Magnetic Field Analysis (UP19980818) (Site not responding. Last check: 2007-10-14)
		Magnetic fields may exist as a result of an electric current, a permanent magnet, or an applied external field.
		Depending on the element type and element option you choose, the degrees of freedom may be scalar magnetic potentials, vector magnetic potentials, or edge flux.
		The Magnetic Vector Potential (MVP) formulation is one of the two nodal-based methods for 3-D static, harmonic, and transient analyses which the ANSYS program supports.
	www.uic.edu /depts/accc/software/ansys/html/guide_55/g-ele/GELE1.htm (1327 words)

	The magnetic vector potential
		In other words, the vector potential is undetermined to the gradient of a scalar field.
		Note that the vector potential is parallel to the direction of the current.
		This would seem to suggest that there is a more direct relationship between the vector potential and the current than there is between the magnetic field and the current.
	farside.ph.utexas.edu /teaching/em/lectures/node38.html (631 words)

	Symbolic Analysis of Magnetic Field with
		r x J dv is the magnetic moment of the current distribution (m =iA in the case of a filamentary one-turn coil of area A), relation which shows the decrease of the field inversely proportional to the cube of the distance to the source.
		The vector potential given by (4) is solenoidal (has div A = 0), if the divergence of the current density is zero in the whole conducting domain (respectively, if the normal component of the current density, Jn, is zero on the surface of the conductor).
		In this case, the vector potential has only one component, normal to the problem's plane (A is represented by a scalar rather than a vector), and the magnetic field lines coincide with the equipotential lines.
	www.ewh.ieee.org /soc/es/May2001/03/bsl1.html (1266 words)

	(montalk.net) Research Notes: Transverse Waves
		As mentioned earlier, a current-carrying wire is surrounded by a circular magnetic field due to differences between adjacent parts of the vector potential field creating vorticity.
		In fact, the vector potential is more “real” than either the electric or magnetic fields which are just our measurable interpretations of different distortions in the vector potential.
		Some might respond that the vector potential is just a mathematical convenience, an arbitrary concept with no tangible existence of its own, but that could not be further from the truth.
	montalk.net /notes/transverse-waves (637 words)

	Apartment Buildings and Magnetic Vector Potentials
		They are overcome by magnetic vector potentials and their expressions help us to understand the truth of the world.
		The magnetic potentials impose a phase shift on the electrons found in electric metals, these electromagnetic distortions poison the Holy Spirit.
		For a fire is kindled in mine anger, and shall burn unto the lowest hell, and shall consume the earth with her increase, and set on fire the foundations of the mountains.
	www.thetemple.cc /story/apartment_magnetic_vectors.htm (559 words)

	A Hybrid Magnetic Field Solver Using a Combined Finite Element/Boundary Element Field Solver (Site not responding. Last check: 2007-10-14)
		Of course for a vector potential in 3D there will be three values at each node corresponding to each of the Cartesian coordinate directions.
		To calculate the magnetic field density the vector potential must be differentiated.
		is known, the magnetic potential and the magnetic density are calculated by integrating the unknown.
	www.integratedsoft.com /papers/research/hybrid (2342 words)

	Lectures (Site not responding. Last check: 2007-10-14)
		Derived the expressions for the intrinsic impedance, the input impedance, the input admittance, VSWR and reflection coefficient.
		Derived the expression for time-varying electric field in terms of electric scalar potential and magnetic vector potential.
		Developed electric potential gradient and the differential and integral form relating the vector electric field intensity and the scalar electric potential.
	hal.lamar.edu /~eece/maxum/electromagnetics/lectures.html (1111 words)

	Publication : S99/137 (Site not responding. Last check: 2007-10-14)
		Transfer of energy and magnetic potential is studied in 2D MHD turbulence in the presence of a background shear flow and magnetic field.
		By using a two-scale analysis and the Gabor transform, the direction of the cascade of energy and magnetic vector potential is found to depend on the properties of forcings.
		In particular, in the case of a magnetic forcing that is isotropic, the magnetic vector potential cascades from small to large-scales whereas the energy from large to small-scales.
	www-spht.cea.fr /articles/s99/137 (116 words)

	(montalk.net) Research Notes
		James Clerk Maxwell, the originator of electromagnetic theory, said the vector potential was the most important and fundamental field of electromagnetism and likened it to etheric momentum.
		Gravity is a gradient in the divergence of the magnetic vector potential.
		When the vector potential is strongly and nonlinearly pulsed, it creates a corresponding gravitational pulse because the ether is double compressed.
	www.montalk.net /notes (5421 words)

	4.97 SOLID97 3-D Magnetic Solid (UP19980821 ) (Site not responding. Last check: 2007-10-14)
		SOLID97 is based on the magnetic vector potential formulation with the Coulomb gauge, and is applicable to the following low-frequency magnetic field analyses: magnetostatics, eddy currents (AC time harmonic and transient analyses); voltage forced magnetic fields (static, AC time harmonic and transient analyses); and electromagnetic-circuit coupled fields (static, AC time harmonic and transient analyses).
		Surfaces at which magnetic forces are to be calculated may be identified by using the MXWF label on the surface load commands (no value is required.) A Maxwell stress tensor calculation is performed at these surfaces to obtain the magnetic forces.
		The vector components of the current density are with respect to the element coordinate system (see Section 4.97.3 for solenoidal restriction).
	www.uic.edu /depts/accc/software/ansys/html/elem_55/chapter4/ES4-97.htm (1831 words)

	vector potential of B
		This is more or less the same situation as with the scalar potential V wich can be altered with a constant because that does not change the electric field; this is called a 'gauge freedom'.
		In the case of the magnetic field the relation between the vector potential and the magnetic field is given by:
		I think it is obvious SelfAdjoint misunderstood the question, as he talks about the divergence of the magnetic field and not the divergence of the magnetic vector potential.
	www.physicsforums.com /showthread.php?p=372191 (1115 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		The application of external magnetic field causes both an alignment of the magnetic moments of the spinning electrons and an induced magnetic moment due to a change in the orbital motion of electrons.
		The magnetic field of a small bar magnet is the same as that of a magnetic dipole.
		For a bar magnet the fictitious magnetic charges +qm and —qm are assumed to be separated by a distance d and to form an equivalent magnetic dipole of moment.
	www.ece.sc.edu /classes/Summer01/elct361/EM-CH06.doc (1064 words)

	Méditech SARL, electrical machines and applications
		It uses a magnetic vector potential and modified electrical scalar potential formulation.
		For these problems the program finds a solution for the magnetic vector potential to the equation rot(H(t)) =J(t).
		The program calculates Az(x,y,t), z component of the magnetic vector potential, and Y(t) (modified electric potential: time integrated electric scalar potential) for circuit elements.
	meditech.free.fr /uk/gk_uk.htm (641 words)

	NISA/EMAG: Magnetic Field Analysis (MFIELD)
		Transient magnetic field analysis (TMAG) Computation of magnetic vector potential and fields in magnetic and conducting materials due to transient current excitation.
		Magnetodynamic analysis (MGDN) Computation of magnetic vector potential and fields and eddy currents in magnets and conducting materials due to sinusoidal (ac) current excitation.
		Magnetic flux density distribution in a solenoid (non-linear magnetostatic anlysis)
	www.emrc.com /webpages/emagbroc/mfield.htm (182 words)

	Ongoing Development in NISA/EMAG
		Among the new capabilities being avaliable in the 6.0 release are magnetic vector potential analysis for 3D magnetostatics and 2D and 3D permanent magnet modeling.
		Therefore, the 3D magnetic vector potential approach has been incorporated into NISA/EMAG to allow the user to choose the appropriate method for their specific problem.
		The figure shows the magnetic flux density distribution in a 3D DC generator using the magnetic vector potential approach.
	www.emrc.com /webpages/news/odemag.htm (243 words)

	Lecture 25
		The definition of a vector field requires the specification of both its curl and its divergence.
		A relates to the magnetic flux Φ through a given area S that is bounded by contour C in a simple way
		Example 6-5 The magnetic flux density at the center of a square loop.
	www.ee.umd.edu /class/enee380-1.F2004/lectures/lecture25.htm (323 words)

	DA (Site not responding. Last check: 2007-10-14)
		Magnetic vector potential in X direction (see 4).
		Magnetic vector potential in Z direction (see 1).
		For elements HF119 and HF120, used in high-frequency electromagnetic analysis, the AX DOF is not an x-component of a vector potential, but rather a tangential component of E (the electric field) on the element edges and faces.
	www1.ansys.com /customer/content/documentation/80/ansys/Hlp_C_DA.html (545 words)

	5.4. Voltage Forced and Circuit-Coupled Magnetic Field (Site not responding. Last check: 2007-10-14)
		The magnetic vector potential formulation discussed in Electromagnetics requires electric current density as input.
		Then, by using the magnetic vector potential approach from Electromagnetics, the following element matrix equation is derived.
		The magnetic flux density {B}, the magnetic field intensity {H}, magnetic forces and Joule heat can be calculated from the nodal magnetic vector potential {A} using Equation 5.116 and Equation 5.117.
	www.oulu.fi /atkk/tkpalv/unix/ansys-6.1/content/thy_emg4.html (497 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		This is the same definition for the vector potential that we used in the study of magnetostatics.
		Thus, the potential function, from (5.20), is EMBED Equation.3 (5.22) in the phasor domain, and EMBED Equation.3 (5.23) where EMBED Equation.3 (5.24) is the phase velocity of the outgoing wave in the medium.
		It is usually referred to as a magnetic dipole because the radiated fields that it generates are the magnetic analogue of electric dipole fields.
	www.ece.sc.edu /classes/Spring01/elct362/Ch5_362.doc (5850 words)

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