On the Covariant Representation of Integral Equations of the Electromagnetic Field
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Units and Magnitudes (Lecture Notes)
physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass. -
Weberˇs Planetary Model of the Atom
Weber’s Planetary Model of the Atom Bearbeitet von Andre Koch Torres Assis, Gudrun Wolfschmidt, Karl Heinrich Wiederkehr 1. Auflage 2011. Taschenbuch. 184 S. Paperback ISBN 978 3 8424 0241 6 Format (B x L): 17 x 22 cm Weitere Fachgebiete > Physik, Astronomie > Physik Allgemein schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Weber’s Planetary Model of the Atom Figure 0.1: Wilhelm Eduard Weber (1804–1891) Foto: Gudrun Wolfschmidt in der Sternwarte in Göttingen 2 Nuncius Hamburgensis Beiträge zur Geschichte der Naturwissenschaften Band 19 Andre Koch Torres Assis, Karl Heinrich Wiederkehr and Gudrun Wolfschmidt Weber’s Planetary Model of the Atom Ed. by Gudrun Wolfschmidt Hamburg: tredition science 2011 Nuncius Hamburgensis Beiträge zur Geschichte der Naturwissenschaften Hg. von Gudrun Wolfschmidt, Geschichte der Naturwissenschaften, Mathematik und Technik, Universität Hamburg – ISSN 1610-6164 Diese Reihe „Nuncius Hamburgensis“ wird gefördert von der Hans Schimank-Gedächtnisstiftung. Dieser Titel wurde inspiriert von „Sidereus Nuncius“ und von „Wandsbeker Bote“. Andre Koch Torres Assis, Karl Heinrich Wiederkehr and Gudrun Wolfschmidt: Weber’s Planetary Model of the Atom. Ed. by Gudrun Wolfschmidt. Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften, Band 19. Hamburg: tredition science 2011. Abbildung auf dem Cover vorne und Titelblatt: Wilhelm Weber (Kohlrausch, F. (Oswalds Klassiker Nr. 142) 1904, Frontispiz) Frontispiz: Wilhelm Weber (1804–1891) (Feyerabend 1933, nach S. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Electromagnetic Particles Guy Michel Stephan
Electromagnetic particles Guy Michel Stephan To cite this version: Guy Michel Stephan. Electromagnetic particles. 2017. hal-01446417 HAL Id: hal-01446417 https://hal.archives-ouvertes.fr/hal-01446417 Preprint submitted on 2 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Electromagnetic particles. G.M. St´ephan 26, Chemin de Quo Vadis 22730, Tregastel email : [email protected] 25 janvier 2017 R´esum´e The covariant derivative of the 4-components electromagnetic potential in a flat Minkowski space- time is split into its antisymmetric and symmetric parts. While the former is well known to describe the electromagnetic field, we show that the latter describes the associated particles. When symmetry principles are applied to the invariants in operations of the Poincar´egroup, one finds equations which describe the structure of the particles. Both parts of the tensor unify the concept of matter-wave duality. Charge and mass are shown to be associated to the potential. 1 Introduction. When Born and Infeld published their work[1] on the foundations of non linear electromagnetism in the year 1934, their aim was to describe the electron and more generally the physical world from a purely electromagnetic theory. -
Electromagnetic Forces and Internal Stresses in Dielectric Media
PHYSICAL REVIEW E 85, 046606 (2012) Electromagnetic forces and internal stresses in dielectric media Winston Frias* and Andrei I. Smolyakov Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place Saskatoon, SK S7N 5E2, Canada (Received 16 August 2011; revised manuscript received 26 January 2012; published 23 April 2012) The macroscopic electromagnetic force on dielectric bodies and the related problem of the momentum conservation are discussed. It is argued that different forms of the momentum conservation and, respectively, different forms of the force density, correspond to the different ordering in the macroscopic averaging procedure. Different averaging procedures and averaging length scale assumptions result in expressions for the force density with vastly different force density profiles which can potentially be detected experimentally by measuring the profiles of the internal stresses in the medium. The expressions for the Helmholtz force is generalized for the dissipative case. It is shown that the net (integrated) force on the body in vacuum is the same for Lorentz and Helmholtz expressions in all configuration. The case of a semi-infinite medium is analyzed and it is shown that explicit assumptions on the boundary conditions at infinity remove ambiguity in the force on the semi-infinite dielectric. DOI: 10.1103/PhysRevE.85.046606 PACS number(s): 03.50.De I. INTRODUCTION This article is organized as follows. In Sec. II, the problem of the momentum exchange and the force is explored from Electromagnetic forces on charged particles result in an the microscopic point of view. In Sec. III, the Abraham and overall force imparted on a body that is called radiation Minkowski expressions for the momentum and the stress (ponderomotive) pressure. -
The Energy-Momentum Tensor of Electromagnetic Fields in Matter
The energy-momentum tensor of electromagnetic fields in matter Rodrigo Medina1, ∗ and J Stephany2, † 1Centro de F´ısica, Instituto Venezolano de Investigaciones Cient´ıficas, Apartado 20632 Caracas 1020-A, Venezuela. 2Departamento de F´ısica, Secci´on de Fen´omenos Opticos,´ Universidad Sim´on Bol´ıvar,Apartado Postal 89000, Caracas 1080-A, Venezuela. In this paper we present a complete resolution of the Abraham-Minkowski controversy about the energy-momentum tensor of the electromagnetic field in matter. This is done by introducing in our approach several new aspects which invalidate previous discussions. These are: 1)We show that for polarized matter the center of mass theorem is no longer valid in its usual form. A contribution related to microscopic spin should be considered. This allows to disregard the influencing argument done by Balacz in favor of Abraham’s momentum which discuss the motion of the center of mass of light interacting with a dielectric block. 2)The electromagnetic dipolar energy density −P · E contributes to the inertia of matter and should be incorporated covariantly to the the energy- momentum tensor of matter. This implies that there is also an electromagnetic component in matter’s momentum density given by P × B which accounts for the diference between Abraham and Minkowski’s momentum densities. The variation of this contribution explains the results of G. B. Walker, D. G. Lahoz and G. Walker’s experiment which until now was the only undisputed support to Abraham’s force. 3)A careful averaging of microscopic Lorentz’s force results in the µ 1 µ αβ unambiguos expression fd = 2 Dαβ ∂ F for the force density which the field exerts on matter. -
Units and Magnitudes (Lecture Notes)
physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass. -
Vocabulary of Magnetism
TECHNotes The Vocabulary of Magnetism Symbols for key magnetic parameters continue to maximum energy point and the value of B•H at represent a challenge: they are changing and vary this point is the maximum energy product. (You by author, country and company. Here are a few may have noticed that typing the parentheses equivalent symbols for selected parameters. for (BH)MAX conveniently avoids autocorrecting Subscripts in symbols are often ignored so as to the two sequential capital letters). Units of simplify writing and typing. The subscripted letters maximum energy product are kilojoules per are sometimes capital letters to be more legible. In cubic meter, kJ/m3 (SI) and megagauss•oersted, ASTM documents, symbols are italicized. According MGOe (cgs). to NIST’s guide for the use of SI, symbols are not italicized. IEC uses italics for the main part of the • µr = µrec = µ(rec) = recoil permeability is symbol, but not for the subscripts. I have not used measured on the normal curve. It has also been italics in the following definitions. For additional called relative recoil permeability. When information the reader is directed to ASTM A340[11] referring to the corresponding slope on the and the NIST Guide to the use of SI[12]. Be sure to intrinsic curve it is called the intrinsic recoil read the latest edition of ASTM A340 as it is permeability. In the cgs-Gaussian system where undergoing continual updating to be made 1 gauss equals 1 oersted, the intrinsic recoil consistent with industry, NIST and IEC usage. equals the normal recoil minus 1. -
Introduction to Electrostatics
Introduction to Electrostatics Charles Augustin de Coulomb (1736 - 1806) December 23, 2000 Contents 1 Coulomb's Law 2 2 Electric Field 4 3 Gauss's Law 7 4 Di®erential Form of Gauss's Law 9 5 An Equation for E; the Scalar Potential 10 r £ 5.1 Conservative Potentials . 11 6 Poisson's and Laplace's Equations 13 7 Energy in the Electric Field; Capacitance; Forces 15 7.1 Conductors . 20 7.2 Forces on Charged Conductors . 22 1 8 Green's Theorem 27 8.1 Green's Theorem . 29 8.2 Applying Green's Theorem 1 . 30 8.3 Applying Green's Theorem 2 . 31 8.3.1 Greens Theorem with Dirichlet B.C. 34 8.3.2 Greens Theorem with Neumann B.C. 36 2 We shall follow the approach of Jackson, which is more or less his- torical. Thus we start with classical electrostatics, pass on to magneto- statics, add time dependence, and wind up with Maxwell's equations. These are then expressed within the framework of special relativity. The remainder of the course is devoted to a broad range of interesting and important applications. This development may be contrasted with the more formal and el- egant approach which starts from the Maxwell equations plus special relativity and then proceeds to work out electrostatics and magneto- statics - as well as everything else - as special cases. This is the method of e.g., Landau and Lifshitz, The Classical Theory of Fields. The ¯rst third of the course, i.e., Physics 707, deals with physics which should be familiar to everyone; what will perhaps not be familiar are the mathematical techniques and functions that will be introduced in order to solve certain kinds of problems. -
Magnetic Immunity of the MRAM Devices
APPLICATION NOTE AN-MEM-003 Magnetic Immunity of the MRAM Devices Table 1: Cross Reference of Applicable Products Product Name Manufacturer Part Number SMD # Device Type Internal PIC# 16Mb MRAM Device UT8MR2M8 5962-12227 01 WP01 64Mb MRAM Device UT8MR8M8 5962-13207 01 MQ09 *PIC = Product Identification Code 1.0 Overview CAES Colorado Springs offers a 16Mb and 64Mb Non-Volatile Magnetoresistive Random Access Memory (MRAM) device. The MRAM devices are designed specifically for operation in both HiRel and Space environments. This application note addresses concerns with the magnetic immunity of these devices. CAES has determined that the MRAM devices have no magnetic risk in the space environment and recommends proper handling to address terrestrial environments. 2.0 Magnetic Fields All magnetic fields are caused by electrical charge in motion. Even the fields from a stationary permanent magnet RELEASED RELEASED are the result of the rotation (quantum spin) of electrons within the material. There are two "components" of a magnetic field which are both commonly called "magnetic field." They are the B field (historically called Magnetic Induction) and the H field (historically called Magnetic Field). They are related by the equation B = H + 4pM where M is a term called "Magnetization" or "Magnetic Polarization" and is a property of the materials through which the 11 fields pass. Technically, M is the magnetic moment of the material per unit volume. To obtain the total B field, if considering the field in a volume of space, the free (unbound field) H plus the bound fields (magnetic dipoles) M / 13 must be known. -
Formulation of Energy Momentum Tensor for Generalized Fields of Dyons
Formulation of Energy Momentum Tensor for Generalized fields of dyons Gaurav Karnatak∗, P. S. Bisht∗, O. P. S. Negi∗ November 26, 2016 ∗Department of Physics Kumaun University S. S. J. Campus Almora-263601(Uttarakhand) India Email- [email protected] [email protected] [email protected] Abstract The energy momentum tensor of generalized fields of dyons and energy momentum conservation laws of dyons has been developed in simple, compact and consistent manner. We have obtained the Maxwell’s field theory of energy momentum tensor of dyons (electric and magnetic) of electromagnetic field, Poynting vector and Poynting theorem for generalized fields of dyons in a simple, unique and consistent way. Keywords: Dyons, Electromagnetic fields, Energy-momentum tensor, Poynting vector. 1 Introduction The concept of the energy-momentum tensor in classical field theory has a long history, especially in Ein- stein’s theory of gravity [1]. The energy-momentum tensor combines the densities and flux densities of energy and momentum of the fields into one single object. The problem of giving a concise definition of this object able to provide the physically correct answer under all circumstances, for an arbitrary Lagrangian field theory on an arbitrary space-time background, has puzzled physicists for decades. The classical field theory with space-time translation invariance has a conserved energy-momentum tensor [1, 2]. The classical Lagrangian in constructing the energy-momentum tensor, like the canonical energy-momentum tensor was noticed long ago. The question is based on the Noethern theorem, according to which a field theory with space-time translation invariance has a conserved energy-momentum tensor. -
The International System of Units (SI) - Conversion Factors For
NIST Special Publication 1038 The International System of Units (SI) – Conversion Factors for General Use Kenneth Butcher Linda Crown Elizabeth J. Gentry Weights and Measures Division Technology Services NIST Special Publication 1038 The International System of Units (SI) - Conversion Factors for General Use Editors: Kenneth S. Butcher Linda D. Crown Elizabeth J. Gentry Weights and Measures Division Carol Hockert, Chief Weights and Measures Division Technology Services National Institute of Standards and Technology May 2006 U.S. Department of Commerce Carlo M. Gutierrez, Secretary Technology Administration Robert Cresanti, Under Secretary of Commerce for Technology National Institute of Standards and Technology William Jeffrey, Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. National Institute of Standards and Technology Special Publications 1038 Natl. Inst. Stand. Technol. Spec. Pub. 1038, 24 pages (May 2006) Available through NIST Weights and Measures Division STOP 2600 Gaithersburg, MD 20899-2600 Phone: (301) 975-4004 — Fax: (301) 926-0647 Internet: www.nist.gov/owm or www.nist.gov/metric TABLE OF CONTENTS FOREWORD.................................................................................................................................................................v