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	Vector potential - Wikipedia, the free encyclopedia
		In vector calculus, a vector potential is a vector field whose curl is a given vector field.
		This is analogous to a scalar potential, which is a scalar field whose negative gradient is a given vector field.
		A generalization of this theorem is the Helmholtz decomposition which states that any vector field can be decomposed as a sum of a solenoidal vector field and an irrotational vector field.
	en.wikipedia.org /wiki/Vector_potential (247 words)

	Encyclopedia: Vector potential
		Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space.
		A scalar potential is, mathematically, a scalar field whose negative gradient is a given vector field.
		The Helmholtz decomposition of a vector field which is twice continuously differentiable, with rapid enough decay at infinity, splits the vector field into a sum of gradient and curl as follows: where represents the Newtonian potential.
	www.nationmaster.com /encyclopedia/Vector-potential (577 words)

	Magnetic Vector Potential (Site not responding. Last check: 2007-10-22)
		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)

	[No title]
		H was portrayed as the curl of another vector, the vector potential A.
		The boundary conditions obeyed by the vector potential at surfaces of discontinuity (containing surface currents) reflect the discontinuity in tangential H field and the continuity of the normal flux density.
		The vector potential is similarly related to the terminal characteristics of a lumped parameter element, this time an inductor.
	web.mit.edu /6.013_book/www/chapter8/8.7.html (896 words)

	Vector potential -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		In (Click link for more info and facts about vector calculus) vector calculus, a vector potential is a (Click link for more info and facts about vector field) vector field which generates a (Click link for more info and facts about solenoidal vector field) solenoidal vector field.
		This vector potential always points downwards (-z direction) but its magnitude is a radial (Click link for more info and facts about Gaussian function) Gaussian function, centered at the z axis, with inflection points around in a circle of radius 1.
		Now walk from that point towards the +j direction; if the potential is not saddle-shaped (assume it is not, because the starting point was the maximum) then the A pillars decrease in height further contributing a dyadic term.
	www.absoluteastronomy.com /encyclopedia/v/ve/vector_potential.htm (1297 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.
		A/∂t) is a potential vector because its curl vanishes.
	wheger.tripod.com /thesis/htm/th2.htm (2592 words)

	Potential
		Technically, it is a scalar field used to describe a conservative (curl-free) vector field V, such that the vector field is the gradient of the potential (possibly multiplied by a constant).
		A related concept is that of a vector potential: a vector field describing a divergence free vector field (having only "closed" field lines) that is its curl.
		This potential is also generalized for the case of circuits with inductance, handling the case of non-conservative electric fields (which occur when there is a time-varying magnetic flux), by including an effective potential difference equal to the integral of electric field around the closed circuit (zero for a conservative field).
	www.brainyencyclopedia.com /encyclopedia/p/po/potential.html (444 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 4-Potential Representation of Newtonian Gravity
		These potentials have a meaning similar to that of the retarded potentials of the Liénard-Wiechert [3] equations for charge, which in turn are the same as those of the potential representation of the Maxwell equations.
		The gauge transformed potential does not decay with distance, but the potentials are not directly measurable, and the acceleration field decays approximately by the inverse square law in either gauge.
		The potential at the field point must be taken as existing at the advanced time in performing the transformation.
	www.s-4.com /retard/static (725 words)

	Scalar Potential versus Vector Field (Site not responding. Last check: 2007-10-22)
		Whether we used discrete superposition (adding the fields of discrete charges), continuous superposition (integrating to sum the fields of all the tiny differential chunks of a charge density distribution) or Gauss's Law for the three highly symmetric charge distributions, there is some possibly fairly serious calculus and geometry involved.
		Fortunately, we are now ready to pitch this vector description in favor of a scalar description.
		The scalar description will in some sense be ``more fundamental'' than the vector description, in that one will be able to obtain the vector description from the scalar description by (relatively simple) differentiation.
	www.phy.duke.edu /~rgb/Class/phy42/node11.html (395 words)

	Articles - Magnetic potential (Site not responding. Last check: 2007-10-22)
		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.
		The former method is more popular because the scalar electric potential is widely familiar as voltage and because the concept of vector electric potential is just too weird to exist in the same universe as decent common-sense folks.
	www.gaple.com /articles/Magnetic_potential (639 words)

	Determinateness of the Complex Potential Function Vector (Site not responding. Last check: 2007-10-22)
		We consider the uniqueness of the complex potential function vector for a given state of stress.
		is determined except for a pure imaginary constant vector.
		Since the stress is completely determined from equation (6) when the stress function vector is given, we substitute the complex potential vector (51) into question (13) and compare the result with its expected form (48) to get
	www.rci.rutgers.edu /~denda/notes/aniso1/node12.html (536 words)

	The magnetic vector potential (Site not responding. Last check: 2007-10-22)
		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/em1/lectures/node35.html (641 words)

	Magnetic Induction and Inductors
		Inductance is the tendency of a current in a conductor to maintain itself in the face of changes in the potential difference driving the current.
		The sum is obtained by the vector addition of the two components.
		Above and below the plates the magnetic field is zero because the vector potential is constant.
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node185.html (493 words)

	Urban Entomology [Ebeling Chap. 9 part 3] Pests Attacking Mand and His Pets (Site not responding. Last check: 2007-10-22)
		The potentially long pupal stage, besides the fact that adult fleas can live without food for remarkably long periods, accounts for the fact that people may enter a house after it has been unoccupied by humans or pets for months, yet be rapidly and severely attacked by fleas.
		The oriental rat flea is also the principal vector of murine or endemic typhus that may be transmitted from rats to man. This disease is caused by the microorganism Rickettsia mooseri, and is widespread in rats and other rodents.
		They are potential transmitters of plague and murine typhus, but the habit of the females of remaining fastened to a single, host most of their lives greatly decreases their importance in this respect.
	www.entomology.ucr.edu /ebeling/ebel9-3.html (19692 words)

	Scalar Waves/Aharonov-Bohm Effect/A-Vector Potential
		Surprisingly the Li'enard-Wiechert potentials do not satisfy the Lorenz gauge condition, therefore they cannot be regarded as solutions of the Maxwell equations in the Lorenz gauge, but only as solutions of the inhomogeneous potential wave equations.
		Therefore, the inhomogeneous potential wave equations should be regarded as a separate set of differential equation that are unconnected with Maxwell's equations.
		In order to simplify this theory of classical electrodynamics we propose a generalization of Maxwell's equations, such that a gauge of the potentials is unnecessary in order to derive the Lorenz inhomogeneous potential wave equations.
	www.unusualresearch.com /scalarbib/scalarbib.htm (895 words)

	JLN Labs - Patents list about Vector Potential (Site not responding. Last check: 2007-10-22)
		The system includes apparatus for detecting the curl-free magnetic vector potential field component by means of a Josephson junction.
		The magnetic vector potential field interacts with the Josephson junction by varying the phase of the argument of the sine function which determines the Josephson junction current.
		Because the magnitude of the change in the detected curl-free vector potential field causes a proportional change in the phase of the Josephson junction current, the modulation of the field can be established.
	jnaudin.free.fr /html/tepvppl.htm (252 words)

	[No title]
		One of the following fields is derivable from a scalar potential but not a vector potential; one is derivable from a vector potential but not a scalar potential.
		Evaluate the line integrals ((F(dR, for each of the 2 vector fields in Problem 1, where (is the curve parametrized by R = ti + j + t2k (0 (t (1).
		You need not carry out the final integrations, but to get full credit you must use the potentials you found in Problem 1 when they are applicable.
	ee.eng.usf.edu /people/snider/5421/EGN5421Final02b.doc (277 words)

	Physics Help and Math Help - Physics Forums - Merged Magnetism Thread
		All the magnetic field would be contained in the body of the loop but outside the loop you would have a vector potential circulating around the body of the loop.
		The reason the vector potential exists is because the magnetic field is divergence free.
		You can start with the pair of monopoles in empty space and ask the very same question about what happens to the vector potential, but the magnetic loop makes it much easier to see the double connectivity that is such an important part of the magnetic field, and its role regarding the vector potential.
	www.physicsforums.com /printthread.php?t=4474&pp=40 (2590 words)

	Reconstructed Potential Functions In Bounded Domain Vector Tomography - Osman, Prince (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Abstract: The tomographic imaging of vector fields on bounded domains is considered.
		It is then shown that potential functions reconstructed from these formulas include a component that arises from the harmonic component of the vector field, which is due to boundary conditions alone.
		Closed form expressions for the harmonic field contribution to the reconstructed scalar and vector potential functions are...
	citeseer.ist.psu.edu /osman97reconstructed.html (478 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		This is the same definition for the vector potential that we used in the study of magnetostatics.
		Similarly, by substituting for EMBED Equation.3 in (5.4) and applying the Lorentz condition, we obtain a wave equation in terms of the scalar potential V as EMBED Equation.3 (5.14) Equations (5.13) and (5.14) are known as the inhomogeneous Helmholtz equations in terms of potential functions.
		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.
	www.ece.sc.edu /classes/Spring01/elct362/Ch5_362.doc (5850 words)

	Corner Detection Via Topographic Analysis of Vector Potential (Site not responding. Last check: 2007-10-22)
		In our previous work we demonstrated that edges are the local maxima of the vector potential while points of symmetry correspond to the local minimum.
		In this paper we demonstrate that corners are located at the saddle points of the magnitude of the vector potential.
		This involves performing a non-minimum suppression test in the direction of the vector potential and a non-maximum suppression test in the orthogonal direction.
	www.bmva.ac.uk /bmvc/1998/papers/d148/h148.htm (220 words)

	Vector Potential (Site not responding. Last check: 2007-10-22)
		This can be checked by using a flip-coil, Hall probe, or compass needle near the toroidal coil.
		However, the lines of vector potential circle the flux lines:
		If a wire is threaded through the hole of the toroid and returned through the hole, case 1, no galvanometer deflection is seen as B is switched on and off.
	www.physics.ucla.edu /demoweb/demomanual/electricity_and_magnetism/electrodynamics/vector_potential.html (104 words)

	Constrained Motion Control Using Vector Potential Fields - Masoud, Masoud (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Abstract: This paper discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and well-behaved path to a desired target.
		The most significant tool is the artificial vector potential field which shows a better ability to steer motion than does a scalar potential field.
		39 Potential field methods and their inherent limitations for m..
	citeseer.ist.psu.edu /masoud00constrained.html (1208 words)

	"Genetically Modified Plants and the 35S Promoter: Assessing the Risks and Enhancing the Debate"
		In this article, we discuss the properties of CaMV and the 35S promoter and the potential risks associated with the use of the promoter in GM plants, concluding that any risks are no greater than those encountered in conventional plant breeding.
		This is exemplified by the attempts to use cauliflower mosaic virus as a gene vector (see Hull, 1983).
		Since these potentially carcinogenic compounds have not been implicated in causing human cancers, it is considered that humans are more adapted to them.
	www.biotech-info.net /enhancing_debate.html (3354 words)

	Articles - Potential (Site not responding. Last check: 2007-10-22)
		In addition to this scalar potential, the vector potential is a related construct.
		As entities described as vector fields occur often in physics, it is often useful to work with their potentials.
		In quantum theory, gauge invariance leads to Aharonov-Bohm effects where an effect of a potential is observable even in regions where the corresponding classical field is zero.
	www.gaple.com /articles/Potential?mySession=459fa86478588d87f7e79f28d7d6fb54 (505 words)

	Experiment on Vector Potential by Jean-Louis Naudin
		This simple experiment is a replication of the Quadra test done by Telos Research on 'Toroid coils and Vector Potential'.
		Today, after a lot of tests conducted on the Telos' Toroid coils, it seems that the effects observed are relevant to a common Lenz repulsion force produced by the leakage of the magnetic field produced by a saturation of the ferrite core.
		A true action of the Magnetic Vector Potential has not yet been detected in the Telos' toroid coils device.
	jlnlabs.imars.com /vpexp (803 words)

	Magnetic Vector Potential (Site not responding. Last check: 2007-10-22)
		Magnetic Vector Potential -- from Eric Weisstein's World of Physics...
		vector potential of B - Information Technology Services...
		Welcome to IEEE Xplore 2.0: Further discussion on magnetic vector potential fini...
	www.scienceoxygen.com /phys/114.html (196 words)

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