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Masud Mansuripur - One of the best experts on this subject based on the ideXlab platform.
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Force torque linear momentum and angular momentum in classical electrodynamics
Applied Physics A, 2017Co-Authors: Masud MansuripurAbstract:The classical theory of electrodynamics is built upon Maxwell’s equations and the concepts of electromagnetic (EM) field, Force, energy, and momentum, which are intimately tied together by Poynting’s theorem and by the Lorentz Force Law. Whereas Maxwell’s equations relate the fields to their material sources, Poynting’s theorem governs the flow of EM energy and its exchange between fields and material media, while the Lorentz Law regulates the back-and-forth transfer of momentum between the media and the fields. An alternative Force Law, first proposed by Einstein and Laub, exists that is consistent with Maxwell’s equations and complies with the conservation Laws as well as with the requirements of special relativity. While the Lorentz Law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetized medium, the Einstein–Laub (E–L) formulation of EM Force and torque does not invoke hidden entities under such circumstances. Moreover, total Force/torque exerted by EM fields on any given object turns out to be independent of whether the density of Force/torque is evaluated using the Law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted Force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.
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electric and magnetic dipoles in the Lorentz and einstein laub formulations of classical electrodynamics
Proceedings of SPIE, 2015Co-Authors: Masud MansuripurAbstract:The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just as it postulates the existence and properties of electric charges and currents. Maxwell’s macroscopic equations are mathematically exact and self-consistent differential equations that relate the electromagnetic (EM) field to its sources, namely, electric charge-density free, electric current-density free, polarization , and magnetization . At the level of Maxwell’s macroscopic equations, there is no need for models of electric and magnetic dipoles. For example, whether a magnetic dipole is an Amperian current-loop or a Gilbertian pair of north and south magnetic monopoles has no effect on the solution of Maxwell’s equations. Electromagnetic fields carry energy as well as linear and angular momenta, which they can exchange with material media—the seat of the sources of the EM field—thereby exerting Force and torque on these media. In the Lorentz formulation of classical electrodynamics, the electric and magnetic fields, and , exert Forces and torques on electric charge and current distributions. An electric dipole is then modeled as a pair of electric charges on a stick (or spring), and a magnetic dipole is modeled as an Amperian current loop, so that the Lorentz Force Law can be applied to the corresponding (bound) charges and (bound) currents of these dipoles. In contrast, the Einstein-Laub formulation circumvents the need for specific models of the dipoles by simply providing a recipe for calculating the Force- and torque-densities exerted by the and fields on charge, current, polarization and magnetization. The two formulations, while similar in many respects, have significant differences. For example, in the Lorentz approach, the Poynting vector is = 0 −1 × , and the linear and angular momentum densities of the EM field are = 0 × and = × , whereas in the Einstein-Laub formulation the corresponding entities are = × , = × ⁄2, and = × . (Here 0 and 0 are the permeability and permittivity of free space, is the speed of light in vacuum, = 0 + , and is the position vector.) Such differences can be reconciled by recognizing the need for the so-called hidden energy and hidden momentum associated with Amperian current loops of the Lorentz formalism. (Hidden entities of the sort do not arise in the Einstein-Laub treatment of magnetic dipoles.) Other differences arise from over-simplistic assumptions concerning the equivalence between free charges and currents on the one hand, and their bound counterparts on the other. A more nuanced treatment of EM Force and torque densities exerted on polarization and magnetization in the Lorentz approach would help bridge the gap that superficially separates the two formulations. Atoms and molecules may collide with each other and, in general, material constituents can exchange energy, momentum, and angular momentum via direct mechanical interactions. In the case of continuous media, elastic and hydrodynamic stresses, phenomenological Forces such as those related to exchange coupling in ferromagnets, etc., subject small volumes of materials to external Forces and torques. Such matter-matter interactions, although fundamentally EM in nature, are distinct from field-matter interactions in classical physics. Beyond the classical regime, however, the dichotomy that distinguishes the EM field from EM sources gets blurred. An electron’s wavefunction may overlap that of an atomic nucleus, thereby initiating a contact interaction between the magnetic dipole moments of the two particles. Or a neutron passing through a ferromagnetic material may give rise to scattering events involving overlaps between the wave-functions of the neutron and magnetic electrons. Such matter-matter interactions exert equal and opposite Forces and/or torques on the colliding particles, and their observable effects often shed light on the nature of the particles involved. It is through such observations that the Amperian model of a magnetic dipole has come to gain prominence over the Gilbertian model. In situations involving overlapping particle wave-functions, it is imperative to take account of the particle-particle interaction energy when computing the scattering amplitudes. As far as total Force and total torque on a given volume of material are concerned, such particle-particle interactions do not affect the outcome of calculations, since the mutual actions of the two (overlapping) particles cancel each other out. Both Lorentz and Einstein-Laub formalisms thus yield the same total Force and total torque on a given volume—provided that hidden entities are properly removed. The Lorentz formalism, with its roots in the Amperian current-loop model, correctly predicts the interaction energy between two overlapping magnetic dipoles 1 and 2 as being proportional to −1 ∙ 2. In contrast, the Einstein-Laub formalism, which is ignorant of such particle-particle interactions, needs to account for them separately.
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mechanical effects of light radiation pressure photon momentum and the Lorentz Force Law
Journal of Physical Chemistry & Biophysics, 2014Co-Authors: Masud MansuripurAbstract:The rays of light carry energy as well as linear and angular momentum. The latter properties are exploited in solar sails, optical tweezers, and micro/nano opto-mechanical motors and actuators. A fundamental characteristic of photons, their momentum in the presence of material media, has been the subject of debate and controversy for more than a century. The socalled Abraham-Minkowski controversy involves theoretical arguments in conjunction with experimental tests to determine whether the vacuum photon momentum must be divided or multiplied by the refractive index of the host medium. Also, momentum conservation is intimately tied to the Force Law that specifies the rate of exchange of electromagnetic and mechanical momentum between light and matter. In this presentation the author will discuss the foundational postulates of the MaxwellLorentz theory of electrodynamics that clarify the prevailing ambiguities and resolve the reigning controversies.
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the Lorentz Force Law and its connections to hidden momentum the einstein laub Force and the aharonov casher effect
arXiv: Classical Physics, 2014Co-Authors: Masud MansuripurAbstract:The Lorentz Force of classical electrodynamics, when applied to magnetic materials, gives rise to hidden energy and hidden momentum. Removing the contributions of hidden entities from the Poynting vector, from the electromagnetic momentum density, and from the Lorentz Force and torque densities simplifies the equations of the classical theory. In particular, the reduced expression of the electromagnetic Force-density becomes very similar (but not identical) to the Einstein-Laub expression for the Force exerted by electric and magnetic fields on a distribution of charge, current, polarization and magnetization. Examples reveal the similarities and differences among various equations that describe the Force and torque exerted by electromagnetic fields on material media. An important example of the simplifications afforded by the Einstein-Laub formula is provided by a magnetic dipole moving in a static electric field and exhibiting the Aharonov-Casher effect.
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the Lorentz Force Law and its connections to hidden momentum the einstein laub Force and the aharonov casher effect
IEEE Transactions on Magnetics, 2014Co-Authors: Masud MansuripurAbstract:The Lorentz Force of classical electrodynamics, when applied to magnetic materials, gives rise to hidden energy and hidden momentum. Removing the contributions of hidden entities from the Poynting vector, from the electromagnetic (EM) momentum density, and from the Lorentz Force and torque densities simplifies the equations of the classical theory. In particular, the reduced expression of the EM Force density becomes very similar (but not identical) to the Einstein-Laub expression for the Force exerted by electric and magnetic fields on a distribution of charge, current, polarization, and magnetization. Examples reveal the similarities and differences among various equations that describe the Force and torque exerted by EM fields on material media. An important example of the simplifications afforded by the Einstein-Laub formula is provided by a magnetic dipole moving in a static electric field and exhibiting the Aharonov-Casher effect.
Wonjong Kim - One of the best experts on this subject based on the ideXlab platform.
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design and control of a compact lightweight planar positioner moving over a concentrated field magnet matrix
IEEE-ASME Transactions on Mechatronics, 2013Co-Authors: Vu Huy Nguyen, Wonjong KimAbstract:In this paper, a single-moving-part planar positioner with six coils is designed and implemented. A concentrated-field permanent-magnet matrix is employed as the stationary part. The moving platen has a compact size (185.4 mm × 157.9 mm), light mass (0.64 kg) and low-center-of-gravity. The moving platen carries three planar-motor armatures with two phases per motor. Force calculation is based on the Lorentz Force Law and conducted by volume integration. In order to deal with the nonlinearity due to trigonometric dependencies in the Force-current relation, modified proportional-integral-derivative (PID) and lead-and-PI compensators are designed with computed currents to close the control loop and obtain the desired performances. Experimental results verified the commutation Law and the Force calculation. The new design with only six coils allows for simplification of the control algorithm and reduced power consumption of the positioner. The maximum travel ranges in x, y, and the rotation about the vertical axis are 15.24 cm, 20.32 cm, and 12.03°, respectively. The positioning resolution in x and y is 8 μm with the rms position noise of 6 μm. The positioning resolution in rotations about the vertical axis is 100 μrad.
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novel electromagnetic design for a precision planar positioner moving over a superimposed concentrated field magnet matrix
IEEE Transactions on Energy Conversion, 2012Co-Authors: Vu Huy Nguyen, Wonjong KimAbstract:This paper presents the electromagnetic design and Force calculation of a compact multiaxis precision positioner. A six-coil single-moving-part platen moves over a superimposed concentrated-field permanent-magnet matrix. With a rectangular coil placed in the magnetic field generated by the superimposed concentrated-field magnet matrix, the Force acting on the coil is calculated by volume integration based on the Lorentz Force Law. The distance between the long sides and that between the short sides of a rectangular coil are designed to be a half pitch and one pitch of the magnet matrix, respectively. This allows for the simplification of Force generation and calculation, compact size, and light mass (0.64 kg) of the moving platen. Six coils are divided into three two-phase linear-motor armatures with 270° or 450° phase differences. The complete Force-current relation for the entire platen with the six coils is derived. Experimental results are presented to verify the working principle of the positioner designed in this paper. The positioner can be employed for the stepping and scanning applications that require 3-DOF planar motions with long travel ranges in two horizontal directions and small rotational motions about the vertical axis.
Pablo L Saldanha - One of the best experts on this subject based on the ideXlab platform.
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hidden momentum in a hydrogen atom and the Lorentz Force Law
Physical Review A, 2015Co-Authors: J Oliveira S Filho, Pablo L SaldanhaAbstract:By using perturbation theory, we show that a hydrogen atom with magnetic moment due to the orbital angular momentum of the electron has "hidden momentum" in the presence of an external electric field. This means that the atomic electronic cloud has a nonzero linear momentum in its center-of-mass rest frame due to a relativistic effect. This is completely analogous to the hidden momentum that a classical current loop has in the presence of an external electric field. We discuss that this effect is essential for the validity of the Lorentz Force Law in quantum systems. We also connect our results to the long-standing Abraham-Minkowski debate about the momentum of light in material media.
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division of the momentum of electromagnetic waves in linear media into electromagnetic and material parts
Optics Express, 2010Co-Authors: Pablo L SaldanhaAbstract:It is proposed a natural and consistent division of the momentum of electromagnetic waves in linear, non-dispersive and non-absorptive dielectric and magnetic media into material and electromagnetic parts. The material part is calculated using directly the Lorentz Force Law and the electromagnetic momentum density has the form e0E × B, without an explicit dependence on the properties of the media. The consistency of the treatment is verified through the obtention of a correct momentum balance equation in many examples and showing the compatibility of the division with the Einstein’s theory of relativity by the use of a gedanken experiment. An experimental prediction for the radiation pressure on mirrors immersed in linear dielectric and magnetic media is also made.
Vu Huy Nguyen - One of the best experts on this subject based on the ideXlab platform.
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design and control of a compact lightweight planar positioner moving over a concentrated field magnet matrix
IEEE-ASME Transactions on Mechatronics, 2013Co-Authors: Vu Huy Nguyen, Wonjong KimAbstract:In this paper, a single-moving-part planar positioner with six coils is designed and implemented. A concentrated-field permanent-magnet matrix is employed as the stationary part. The moving platen has a compact size (185.4 mm × 157.9 mm), light mass (0.64 kg) and low-center-of-gravity. The moving platen carries three planar-motor armatures with two phases per motor. Force calculation is based on the Lorentz Force Law and conducted by volume integration. In order to deal with the nonlinearity due to trigonometric dependencies in the Force-current relation, modified proportional-integral-derivative (PID) and lead-and-PI compensators are designed with computed currents to close the control loop and obtain the desired performances. Experimental results verified the commutation Law and the Force calculation. The new design with only six coils allows for simplification of the control algorithm and reduced power consumption of the positioner. The maximum travel ranges in x, y, and the rotation about the vertical axis are 15.24 cm, 20.32 cm, and 12.03°, respectively. The positioning resolution in x and y is 8 μm with the rms position noise of 6 μm. The positioning resolution in rotations about the vertical axis is 100 μrad.
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novel electromagnetic design for a precision planar positioner moving over a superimposed concentrated field magnet matrix
IEEE Transactions on Energy Conversion, 2012Co-Authors: Vu Huy Nguyen, Wonjong KimAbstract:This paper presents the electromagnetic design and Force calculation of a compact multiaxis precision positioner. A six-coil single-moving-part platen moves over a superimposed concentrated-field permanent-magnet matrix. With a rectangular coil placed in the magnetic field generated by the superimposed concentrated-field magnet matrix, the Force acting on the coil is calculated by volume integration based on the Lorentz Force Law. The distance between the long sides and that between the short sides of a rectangular coil are designed to be a half pitch and one pitch of the magnet matrix, respectively. This allows for the simplification of Force generation and calculation, compact size, and light mass (0.64 kg) of the moving platen. Six coils are divided into three two-phase linear-motor armatures with 270° or 450° phase differences. The complete Force-current relation for the entire platen with the six coils is derived. Experimental results are presented to verify the working principle of the positioner designed in this paper. The positioner can be employed for the stepping and scanning applications that require 3-DOF planar motions with long travel ranges in two horizontal directions and small rotational motions about the vertical axis.
Mansuripur Masud - One of the best experts on this subject based on the ideXlab platform.
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Force, torque, linear momentum, and angular momentum in classical electrodynamics
'Springer Science and Business Media LLC', 2017Co-Authors: Mansuripur MasudAbstract:The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, Force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz Force Law. Whereas Maxwell's equations relate the fields to their material sources, Poynting's theorem governs the flow of EM energy and its exchange between fields and material media, while the Lorentz Law regulates the back-and-forth transfer of momentum between the media and the fields. An alternative Force Law, first proposed by Einstein and Laub, exists that is consistent with Maxwell's equations and complies with the conservation Laws as well as with the requirements of special relativity. While the Lorentz Law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetized medium, the Einstein-Laub (E-L) formulation of EM Force and torque does not invoke hidden entities under such circumstances. Moreover, total Force/torque exerted by EM fields on any given object turns out to be independent of whether the density of Force/torque is evaluated using the Law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted Force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.12 month embargo; published online: 19 September 2017This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu
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Force, Torque, Linear Momentum, and Angular Momentum in Classical Electrodynamics
'Springer Science and Business Media LLC', 2017Co-Authors: Mansuripur MasudAbstract:The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, Force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz Force Law. Whereas Maxwell's equations relate the fields to their material sources, Poynting's theorem governs the flow of EM energy and its exchange between fields and material media, while the Lorentz Law regulates the back-and-forth transfer of momentum between the media and the fields. An alternative Force Law, first proposed by Einstein and Laub, exists that is consistent with Maxwell's equations and complies with the conservation Laws as well as with the requirements of special relativity. While the Lorentz Law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetized medium, the Einstein-Laub (E-L) formulation of EM Force and torque does not invoke hidden entities under such circumstances. Moreover, total Force/torque exerted by EM fields on any given object turns out to be independent of whether the density of Force/torque is evaluated using the Law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted Force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.Comment: 15 pages, 35 equations, 75 references. Significant overlap with arXiv:1312.3262, which is the conference proceedings version of this paper. The conference paper, entitled "The Force Law of Classical Electrodynamics: Lorentz versus Einstein and Laub," was published in the Proceedings of SPIE 8810, 88100K-1:18 (2013). arXiv admin note: text overlap with arXiv:1409.479
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Nature of the electromagnetic Force between classical magnetic dipoles
'SPIE-Intl Soc Optical Eng', 2017Co-Authors: Mansuripur MasudAbstract:The Lorentz Force Law of classical electrodynamics states that the Force F exerted by the magnetic induction B on a particle of charge q moving with velocity V is given by F=qVxB. Since this Force is orthogonal to the direction of motion, the magnetic field is said to be incapable of performing mechanical work. Yet there is no denying that a permanent magnet can readily perform mechanical work by pushing/pulling on another permanent magnet -- or by attracting pieces of magnetizable material such as scrap iron or iron filings. We explain this apparent contradiction by examining the magnetic Lorentz Force acting on an Amperian current loop, which is the model for a magnetic dipole. We then extend the discussion by analyzing the Einstein-Laub model of magnetic dipoles in the presence of external magnetic fields.Comment: 6 pages, 2 figures, 20 equations, 6 reference
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Nature of the electromagnetic Force between classical magnetic dipoles
'SPIE-Intl Soc Optical Eng', 2017Co-Authors: Mansuripur MasudAbstract:The Lorentz Force Law of classical electrodynamics states that the Force F exerted by the magnetic induction B on a particle of charge q moving with velocity V is given by F = qV x B Since this Force is orthogonal to the direction of motion, the magnetic field is said to be incapable of performing mechanical work. Yet there is no denying that a permanent magnet can readily perform mechanical work by pushing/pulling on another permanent magnet - or by attracting pieces of magnetizable material such as scrap iron or iron filings. We explain this apparent contradiction by examining the magnetic Lorentz Force acting on an Amperian current loop, which is the model for a magnetic dipole. We then extend the discussion by analyzing the Einstein-Laub model of magnetic dipoles in the presence of external magnetic fields.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu
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On the Electrodynamics of Moving Permanent Dipoles in External Electromagnetic Fields
'SPIE-Intl Soc Optical Eng', 2014Co-Authors: Mansuripur MasudAbstract:The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, Force, energy and momentum, which are intimately tied together by Poynting's theorem and the Lorentz Force Law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz Law regulates the back-and-forth transfer of momentum between the media and the fields. The close association of momentum with energy thus demands that the Poynting theorem and the Lorentz Law remain consistent with each other, while, at the same time, ensuring compliance with the conservation Laws of energy, linear momentum, and angular momentum. This paper shows how a consistent application of the aforementioned Laws of electrodynamics to moving permanent dipoles (both electric and magnetic) brings into play the rest-mass of the dipoles. The rest mass must vary in response to external electromagnetic fields if the overall energy of the system is to be conserved. The physical basis for the inferred variations of the rest-mass appears to be an interference between the internal fields of the dipoles and the externally applied fields. We use two different formulations of the classical theory in which energy and momentum relate differently to the fields, yet we find identical behavior for the rest-mass in both formulations.Comment: 29 pages, 5 figures, 105 equations, 2 appendices, 67 reference
