Weber's Law and Mach's Principle
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Retarded Potentials and Power Emission by Accelerated Charges
Alma Mater Studiorum Universita` di Bologna · Scuola di Scienze Dipartimento di Fisica e Astronomia Corso di Laurea in Fisica Classical Electrodynamics: Retarded Potentials and Power Emission by Accelerated Charges Relatore: Presentata da: Prof. Roberto Zucchini Mirko Longo Anno Accademico 2015/2016 1 Sommario. L'obiettivo di questo lavoro ´equello di analizzare la potenza emes- sa da una carica elettrica accelerata. Saranno studiati due casi speciali: ac- celerazione lineare e accelerazione circolare. Queste sono le configurazioni pi´u frequenti e semplici da realizzare. Il primo passo consiste nel trovare un'e- spressione per il campo elettrico e il campo magnetico generati dalla carica. Questo sar´areso possibile dallo studio della distribuzione di carica di una sor- gente puntiforme e dei potenziali che la descrivono. Nel passo successivo verr´a calcolato il vettore di Poynting per una tale carica. Useremo questo risultato per trovare la potenza elettromagnetica irradiata totale integrando su tutte le direzioni di emissione. Nell'ultimo capitolo, infine, faremo uso di tutto ci´oche ´e stato precedentemente trovato per studiare la potenza emessa da cariche negli acceleratori. 4 Abstract. This paper’s goal is to analyze the power emitted by an accelerated electric charge. Two special cases will be scrutinized: the linear acceleration and the circular acceleration. These are the most frequent and easy to realize configurations. The first step consists of finding an expression for electric and magnetic field generated by our charge. This will be achieved by studying the charge distribution of a point-like source and the potentials that arise from it. The following step involves the computation of the Poynting vector. -
Arxiv:Physics/0303103V3
Comment on ‘About the magnetic field of a finite wire’∗ V Hnizdo National Institute for Occupational Safety and Health, 1095 Willowdale Road, Morgantown, WV 26505, USA Abstract. A flaw is pointed out in the justification given by Charitat and Graner [2003 Eur. J. Phys. 24, 267] for the use of the Biot–Savart law in the calculation of the magnetic field due to a straight current-carrying wire of finite length. Charitat and Graner (CG) [1] apply the Amp`ere and Biot-Savart laws to the problem of the magnetic field due to a straight current-carrying wire of finite length, and note that these laws lead to different results. According to the Amp`ere law, the magnitude B of the magnetic field at a perpendicular distance r from the midpoint along the length 2l of a wire carrying a current I is B = µ0I/(2πr), while the Biot–Savart law gives this quantity as 2 2 B = µ0Il/(2πr√r + l ) (the right-hand side of equation (3) of [1] for B cannot be correct as sin α on the left-hand side there must equal l/√r2 + l2). To explain the fact that the Amp`ere and Biot–Savart laws lead here to different results, CG say that the former is applicable only in a time-independent magnetostatic situation, whereas the latter is ‘a general solution of Maxwell–Amp`ere equations’. A straight wire of finite length can carry a current only when there is a current source at one end of the wire and a curent sink at the other end—and this is possible only when there are time-dependent net charges at both ends of the wire. -
On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch
Andre Koch Torres Assis On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch Abstract The electrostatic, electrodynamic and electromagnetic systems of units utilized during last century by Ampère, Gauss, Weber, Maxwell and all the others are analyzed. It is shown how the constant c was introduced in physics by Weber's force of 1846. It is shown that it has the unit of velocity and is the ratio of the electromagnetic and electrostatic units of charge. Weber and Kohlrausch's experiment of 1855 to determine c is quoted, emphasizing that they were the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchhoff in 1857 and Weber (1857-64) independently of one another obtained the fact that an electromagnetic signal propagates at light velocity along a thin wire of negligible resistivity. They obtained the telegraphy equation utilizing Weber’s action at a distance force. This was accomplished before the development of Maxwell’s electromagnetic theory of light and before Heaviside’s work. 1. Introduction In this work the introduction of the constant c in electromagnetism by Wilhelm Weber in 1846 is analyzed. It is the ratio of electromagnetic and electrostatic units of charge, one of the most fundamental constants of nature. The meaning of this constant is discussed, the first measurement performed by Weber and Kohlrausch in 1855, and the derivation of the telegraphy equation by Kirchhoff and Weber in 1857. Initially the basic systems of units utilized during last century for describing electromagnetic quantities is presented, along with a short review of Weber’s electrodynamics. -
Lawrence Berkeley National Laboratory Recent Work
Lawrence Berkeley National Laboratory Recent Work Title E.E. REVIEW COURSE - LECTURE VIII. Permalink https://escholarship.org/uc/item/733807j5 Authors Martinelli, E. Leppard, J. Perl, H. Publication Date 1952-04-21 eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA UCRT. 1888 Radiation Laboratory Berkeley, California ELECTRICAL ENGINEERING REVIEW COURSE LECTURE VIII April 21, 1952 E. Martinelli (Notes by: J. Leppard, H. -Perl) I. MAG1TETIC FIELDS A. Electrostatic Case Coulomb's Law which is given for th~ electrostatic case can be stated thus~ 2 ~ F = f e1 e2 / r in which F is in dynes, r in centimeters, f = 1 (dimensionless}j'l-gives the value of the charge e, in electro static units (ESU). B. Magnetic Case The magnetic case has an equivalent which was first determined "experi mentally by Ampere. Given two closed loops of wire of length~. Using electromagnetic units (EMU) i is measured in ab amperes = 10 amperes. r is measured in centimeters.· C = 1 (dimensionless). DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. -
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. -
The Fine Structure of Weber's Hydrogen Atom: Bohr–Sommerfeld Approach
Z. Angew. Math. Phys. (2019) 70:105 c 2019 Springer Nature Switzerland AG 0044-2275/19/040001-12 published online June 21, 2019 Zeitschrift f¨ur angewandte https://doi.org/10.1007/s00033-019-1149-4 Mathematik und Physik ZAMP The fine structure of Weber’s hydrogen atom: Bohr–Sommerfeld approach Urs Frauenfelder and Joa Weber Abstract. In this paper, we determine in second order in the fine structure constant the energy levels of Weber’s Hamiltonian that admit a quantized torus. Our formula coincides with the formula obtained by Wesley using the Schr¨odinger equation for Weber’s Hamiltonian. We follow the historical approach of Sommerfeld. This shows that Sommerfeld could have discussed the fine structure of the hydrogen atom using Weber’s electrodynamics if he had been aware of the at-his-time-already- forgotten theory of Wilhelm Weber (1804–1891). Mathematics Subject Classification. 53Dxx, 37J35, 81S10. Keywords. Semiclassical quantization, Integrable system, Hamiltonian system. Contents 1. Introduction 1 2. Weber’s Hamiltonian 3 3. Quantized tori 4 4. Bohr–Sommerfeld quantization 6 Acknowledgements 7 A. Weber’s Lagrangian and delayed potentials 8 B. Proton-proton system—Lorentzian metric 10 References 10 1. Introduction Although Weber’s electrodynamics was highly praised by Maxwell [22,p.XI],seealso[4, Preface],, it was superseded by Maxwell’s theory and basically forgotten. In contrast to Maxwell’s theory, which is a field theory, Weber’s theory is a theory of action-at-a-distance, like Newton’s theory. Weber’s force law can be used to explain Amp`ere’s law and Faraday’s induction law; see [4, Ch. -
The Meaning of the Constant C in Weber's Electrodynamics
Proe. Int. conf. "Galileo Back in Italy - II" (Soc. Ed. Androme-:ia, Bologna, 2000), pp. 23-36, R. Monti (editor) The Meaning of the Constant c in Weber's Electrodynamics A. K. T. Assis' Instituto de Fisica 'Gleb Wat.aghin' Universidade Estadual de Campinas - Unicamp 13083-970 Campinas, Sao Paulo, Brasil Abstract In this work it is analysed three basic electromagnetic systems of units utilized during last century by Ampere, Gauss, Weber, Maxwell and all the others: The electrostatic, electrodynamic and electromagnetic ones. It is presented how the basic equations of electromagnetism are written in these systems (and also in the present day international system of units MKSA). Then it is shown how the constant c was introduced in physics by Weber's force. It is shown that it has the unit of velocity and is the ratio of the electromagnetic and electrostatic Wlits of charge. Weber and Kohlrausch '5 experiment to determine c is presented, emphasizing that they were 'the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchhoff and Weber obtained independently of one another, both working in the framev.-ork of \Veber's electrodynamics, the fact that an electromagnetic signal (of current or potential) propagate at light velocity along a thin wire of negligible resistivity. Key Words: Electromagnetic units, light velocity, wave equation. PACS: O1.55.+b (General physics), 01.65.+g (History of science), 41.20.·q (Electric, magnetic, and electromagnetic fields) ·E-mail: assisOiCLunicamp.br, homepage: www.lCi.unicamp.brrassis AA. VV•. -
Relationships of the SI Derived Units with Special Names and Symbols and the SI Base Units
Relationships of the SI derived units with special names and symbols and the SI base units Derived units SI BASE UNITS without special SI DERIVED UNITS WITH SPECIAL NAMES AND SYMBOLS names Solid lines indicate multiplication, broken lines indicate division kilogram kg newton (kg·m/s2) pascal (N/m2) gray (J/kg) sievert (J/kg) 3 N Pa Gy Sv MASS m FORCE PRESSURE, ABSORBED DOSE VOLUME STRESS DOSE EQUIVALENT meter m 2 m joule (N·m) watt (J/s) becquerel (1/s) hertz (1/s) LENGTH J W Bq Hz AREA ENERGY, WORK, POWER, ACTIVITY FREQUENCY second QUANTITY OF HEAT HEAT FLOW RATE (OF A RADIONUCLIDE) s m/s TIME VELOCITY katal (mol/s) weber (V·s) henry (Wb/A) tesla (Wb/m2) kat Wb H T 2 mole m/s CATALYTIC MAGNETIC INDUCTANCE MAGNETIC mol ACTIVITY FLUX FLUX DENSITY ACCELERATION AMOUNT OF SUBSTANCE coulomb (A·s) volt (W/A) C V ampere A ELECTRIC POTENTIAL, CHARGE ELECTROMOTIVE ELECTRIC CURRENT FORCE degree (K) farad (C/V) ohm (V/A) siemens (1/W) kelvin Celsius °C F W S K CELSIUS CAPACITANCE RESISTANCE CONDUCTANCE THERMODYNAMIC TEMPERATURE TEMPERATURE t/°C = T /K – 273.15 candela 2 steradian radian cd lux (lm/m ) lumen (cd·sr) 2 2 (m/m = 1) lx lm sr (m /m = 1) rad LUMINOUS INTENSITY ILLUMINANCE LUMINOUS SOLID ANGLE PLANE ANGLE FLUX The diagram above shows graphically how the 22 SI derived units with special names and symbols are related to the seven SI base units. In the first column, the symbols of the SI base units are shown in rectangles, with the name of the unit shown toward the upper left of the rectangle and the name of the associated base quantity shown in italic type below the rectangle. -
Mechanical Energy
Chapter 2 Mechanical Energy Mechanics is the branch of physics that deals with the motion of objects and the forces that affect that motion. Mechanical energy is similarly any form of energy that’s directly associated with motion or with a force. Kinetic energy is one form of mechanical energy. In this course we’ll also deal with two other types of mechanical energy: gravitational energy,associated with the force of gravity,and elastic energy, associated with the force exerted by a spring or some other object that is stretched or compressed. In this chapter I’ll introduce the formulas for all three types of mechanical energy,starting with gravitational energy. Gravitational Energy An object’s gravitational energy depends on how high it is,and also on its weight. Specifically,the gravitational energy is the product of weight times height: Gravitational energy = (weight) × (height). (2.1) For example,if you lift a brick two feet off the ground,you’ve given it twice as much gravitational energy as if you lift it only one foot,because of the greater height. On the other hand,a brick has more gravitational energy than a marble lifted to the same height,because of the brick’s greater weight. Weight,in the scientific sense of the word,is a measure of the force that gravity exerts on an object,pulling it downward. Equivalently,the weight of an object is the amount of force that you must exert to hold the object up,balancing the downward force of gravity. Weight is not the same thing as mass,which is a measure of the amount of “stuff” in an object. -
Chapter 6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws
Chapter 6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws 6.1 Displacement Current The magnetic field due to a current distribution satisfies Ampere’s law, (5.45) Using Stokes’s theorem we can transform this equation into an integral form: ∮ ∫ (5.47) We shall examine this law, show that it sometimes fails, and find a generalization that is always valid. Magnetic field near a charging capacitor loop C Fig 6.1 parallel plate capacitor Consider the circuit shown in Fig. 6.1, which consists of a parallel plate capacitor being charged by a constant current . Ampere’s law applied to the loop C and the surface leads to ∫ ∫ (6.1) If, on the other hand, Ampere’s law is applied to the loop C and the surface , we find (6.2) ∫ ∫ Equations 6.1 and 6.2 contradict each other and thus cannot both be correct. The origin of this contradiction is that Ampere’s law is a faulty equation, not consistent with charge conservation: (6.3) ∫ ∫ ∫ ∫ 1 Generalization of Ampere’s law by Maxwell Ampere’s law was derived for steady-state current phenomena with . Using the continuity equation for charge and current (6.4) and Coulombs law (6.5) we obtain ( ) (6.6) Ampere’s law is generalized by the replacement (6.7) i.e., (6.8) Maxwell equations Maxwell equations consist of Eq. 6.8 plus three equations with which we are already familiar: (6.9) 6.2 Vector and Scalar Potentials Definition of and Since , we can still define in terms of a vector potential: (6.10) Then Faradays law can be written ( ) The vanishing curl means that we can define a scalar potential satisfying (6.11) or (6.12) 2 Maxwell equations in terms of vector and scalar potentials and defined as Eqs. -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Presenting Electromagnetic Theory in Accordance with the Principle of Causality Oleg D Jefimenko
Faculty Scholarship 2004 Presenting electromagnetic theory in accordance with the principle of causality Oleg D Jefimenko Follow this and additional works at: https://researchrepository.wvu.edu/faculty_publications Digital Commons Citation Jefimenko, Oleg D, "Presenting electromagnetic theory in accordance with the principle of causality" (2004). Faculty Scholarship. 290. https://researchrepository.wvu.edu/faculty_publications/290 This Article is brought to you for free and open access by The Research Repository @ WVU. It has been accepted for inclusion in Faculty Scholarship by an authorized administrator of The Research Repository @ WVU. For more information, please contact [email protected]. INSTITUTE OF PHYSICS PUBLISHING EUROPEAN JOURNAL OF PHYSICS Eur. J. Phys. 25 (2004) 287–296 PII: S0143-0807(04)69749-2 Presenting electromagnetic theory in accordance with the principle of causality Oleg D Jefimenko Physics Department, West Virginia University, PO Box 6315, Morgantown, WV 26506-6315, USA Received 1 October 2003 Published 28 January 2004 Online at stacks.iop.org/EJP/25/287 (DOI: 10.1088/0143-0807/25/2/015) Abstract Amethod of presenting electromagnetic theory in accordance with the principle of causality is described. Two ‘causal’ equations expressing time-dependent electric and magnetic fields in terms of their causative sources by means of retarded integrals are used as the fundamental electromagnetic equations. Maxwell’s equations are derived from these ‘causal’ equations. Except for the fact that Maxwell’s equations appear as derived equations, the presentation is completely compatible with Maxwell’s electromagnetic theory. An important consequence of this method of presentation is that it offers new insights into the cause-and-effect relations in electromagnetic phenomena and results in simpler derivations of certain electromagnetic equations.