Speed of Light and Maxwell's Constant (Relative Relativity) Introduction
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Basic Magnetic Measurement Methods
Basic magnetic measurement methods Magnetic measurements in nanoelectronics 1. Vibrating sample magnetometry and related methods 2. Magnetooptical methods 3. Other methods Introduction Magnetization is a quantity of interest in many measurements involving spintronic materials ● Biot-Savart law (1820) (Jean-Baptiste Biot (1774-1862), Félix Savart (1791-1841)) Magnetic field (the proper name is magnetic flux density [1]*) of a current carrying piece of conductor is given by: μ 0 I dl̂ ×⃗r − − ⃗ 7 1 - vacuum permeability d B= μ 0=4 π10 Hm 4 π ∣⃗r∣3 ● The unit of the magnetic flux density, Tesla (1 T=1 Wb/m2), as a derive unit of Si must be based on some measurement (force, magnetic resonance) *the alternative name is magnetic induction Introduction Magnetization is a quantity of interest in many measurements involving spintronic materials ● Biot-Savart law (1820) (Jean-Baptiste Biot (1774-1862), Félix Savart (1791-1841)) Magnetic field (the proper name is magnetic flux density [1]*) of a current carrying piece of conductor is given by: μ 0 I dl̂ ×⃗r − − ⃗ 7 1 - vacuum permeability d B= μ 0=4 π10 Hm 4 π ∣⃗r∣3 ● The Physikalisch-Technische Bundesanstalt (German national metrology institute) maintains a unit Tesla in form of coils with coil constant k (ratio of the magnetic flux density to the coil current) determined based on NMR measurements graphics from: http://www.ptb.de/cms/fileadmin/internet/fachabteilungen/abteilung_2/2.5_halbleiterphysik_und_magnetismus/2.51/realization.pdf *the alternative name is magnetic induction Introduction It -
Implementation of the Fizeau Aether Drag Experiment for An
Implementation of the Fizeau Aether Drag Experiment for an Undergraduate Physics Laboratory by Bahrudin Trbalic Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 c Massachusetts Institute of Technology 2020. All rights reserved. ○ Author................................................................ Department of Physics May 8, 2020 Certified by. Sean P. Robinson Lecturer of Physics Thesis Supervisor Certified by. Joseph A. Formaggio Professor of Physics Thesis Supervisor Accepted by . Nergis Mavalvala Associate Department Head, Department of Physics 2 Implementation of the Fizeau Aether Drag Experiment for an Undergraduate Physics Laboratory by Bahrudin Trbalic Submitted to the Department of Physics on May 8, 2020, in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics Abstract This work presents the description and implementation of the historically significant Fizeau aether drag experiment in an undergraduate physics laboratory setting. The implementation is optimized to be inexpensive and reproducible in laboratories that aim to educate students in experimental physics. A detailed list of materials, experi- mental setup, and procedures is given. Additionally, a laboratory manual, preparatory materials, and solutions are included. Thesis Supervisor: Sean P. Robinson Title: Lecturer of Physics Thesis Supervisor: Joseph A. Formaggio Title: Professor of Physics 3 4 Acknowledgments I gratefully acknowledge the instrumental help of Prof. Joseph Formaggio and Dr. Sean P. Robinson for the guidance in this thesis work and in my academic life. The Experimental Physics Lab (J-Lab) has been the pinnacle of my MIT experience and I’m thankful for the time spent there. -
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. -
Magnetism Some Basics: a Magnet Is Associated with Magnetic Lines of Force, and a North Pole and a South Pole
Materials 100A, Class 15, Magnetic Properties I Ram Seshadri MRL 2031, x6129 [email protected]; http://www.mrl.ucsb.edu/∼seshadri/teach.html Magnetism Some basics: A magnet is associated with magnetic lines of force, and a north pole and a south pole. The lines of force come out of the north pole (the source) and are pulled in to the south pole (the sink). A current in a ring or coil also produces magnetic lines of force. N S The magnetic dipole (a north-south pair) is usually represented by an arrow. Magnetic fields act on these dipoles and tend to align them. The magnetic field strength H generated by N closely spaced turns in a coil of wire carrying a current I, for a coil length of l is given by: NI H = l The units of H are amp`eres per meter (Am−1) in SI units or oersted (Oe) in CGS. 1 Am−1 = 4π × 10−3 Oe. If a coil (or solenoid) encloses a vacuum, then the magnetic flux density B generated by a field strength H from the solenoid is given by B = µ0H −7 where µ0 is the vacuum permeability. In SI units, µ0 = 4π × 10 H/m. If the solenoid encloses a medium of permeability µ (instead of the vacuum), then the magnetic flux density is given by: B = µH and µ = µrµ0 µr is the relative permeability. Materials respond to a magnetic field by developing a magnetization M which is the number of magnetic dipoles per unit volume. The magnetization is obtained from: B = µ0H + µ0M The second term, µ0M is reflective of how certain materials can actually concentrate or repel the magnetic field lines. -
The Concept of Field in the History of Electromagnetism
The concept of field in the history of electromagnetism Giovanni Miano Department of Electrical Engineering University of Naples Federico II ET2011-XXVII Riunione Annuale dei Ricercatori di Elettrotecnica Bologna 16-17 giugno 2011 Celebration of the 150th Birthday of Maxwell’s Equations 150 years ago (on March 1861) a young Maxwell (30 years old) published the first part of the paper On physical lines of force in which he wrote down the equations that, by bringing together the physics of electricity and magnetism, laid the foundations for electromagnetism and modern physics. Statue of Maxwell with its dog Toby. Plaque on E-side of the statue. Edinburgh, George Street. Talk Outline ! A brief survey of the birth of the electromagnetism: a long and intriguing story ! A rapid comparison of Weber’s electrodynamics and Maxwell’s theory: “direct action at distance” and “field theory” General References E. T. Wittaker, Theories of Aether and Electricity, Longam, Green and Co., London, 1910. O. Darrigol, Electrodynamics from Ampère to Einste in, Oxford University Press, 2000. O. M. Bucci, The Genesis of Maxwell’s Equations, in “History of Wireless”, T. K. Sarkar et al. Eds., Wiley-Interscience, 2006. Magnetism and Electricity In 1600 Gilbert published the “De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure” (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth). ! The Earth is magnetic ()*+(,-.*, Magnesia ad Sipylum) and this is why a compass points north. ! In a quite large class of bodies (glass, sulphur, …) the friction induces the same effect observed in the amber (!"#$%&'(, Elektron). Gilbert gave to it the name “electricus”. -
Speed Limit: How the Search for an Absolute Frame of Reference in the Universe Led to Einstein’S Equation E =Mc2 — a History of Measurements of the Speed of Light
Journal & Proceedings of the Royal Society of New South Wales, vol. 152, part 2, 2019, pp. 216–241. ISSN 0035-9173/19/020216-26 Speed limit: how the search for an absolute frame of reference in the Universe led to Einstein’s equation 2 E =mc — a history of measurements of the speed of light John C. H. Spence ForMemRS Department of Physics, Arizona State University, Tempe AZ, USA E-mail: [email protected] Abstract This article describes one of the greatest intellectual adventures in the history of mankind — the history of measurements of the speed of light and their interpretation (Spence 2019). This led to Einstein’s theory of relativity in 1905 and its most important consequence, the idea that matter is a form of energy. His equation E=mc2 describes the energy release in the nuclear reactions which power our sun, the stars, nuclear weapons and nuclear power stations. The article is about the extraordinarily improbable connection between the search for an absolute frame of reference in the Universe (the Aether, against which to measure the speed of light), and Einstein’s most famous equation. Introduction fixed speed with respect to the Aether frame n 1900, the field of physics was in turmoil. of reference. If we consider waves running IDespite the triumphs of Newton’s laws of along a river in which there is a current, it mechanics, despite Maxwell’s great equations was understood that the waves “pick up” the leading to the discovery of radio and Boltz- speed of the current. But Michelson in 1887 mann’s work on the foundations of statistical could find no effect of the passing Aether mechanics, Lord Kelvin’s talk1 at the Royal wind on his very accurate measurements Institution in London on Friday, April 27th of the speed of light, no matter in which 1900, was titled “Nineteenth-century clouds direction he measured it, with headwind or over the dynamical theory of heat and light.” tailwind. -
Da Ferraris a Giorgi: La Scuola Italiana Di Elettrotecnica
Da Ferraris a Giorgi: la scuola italiana di Elettrotecnica ADRIANO PAOLO MORANDO Da Ferraris a Giorgi: la scuola italiana di Elettrotecnica Implicita nella Dynamical collocano in modo preciso, facendone Philosophy e nella espansione di una il continuatore, nel solco dell’opera rivoluzione industriale in atto, la nasci- ferrarisiana. Il primo, The foundations ta dell’ingegneria elettrica scientifica si of Electrical Science, del 1894, riporta articolò, postmaxwellianamente, nella a quell’approccio operativo di progressiva transizione dalla figura del- Bridgman che avrebbe in seguito in- lo scienziato (Maxwell), a quella dello fluenzato la lettura di Ercole Bottani. Il scienziato-inventore (Ferraris), a quel- secondo, del 1905, è legato alla Teoria la, infine, del fisico matematico che di- della dinamo ricorsiva, con la quale venta ingegnere (Steinmetz). egli, sulla scia di alcuni contributi Sottolineato lo stretto legame che, ferrarisiani ed anticipando la trasformata sul piano metodologico e fondazionale, di Park, propose un primo approccio correlò la Dynamical Theory maxwel- elettrodinamico alla teoria unificata del- liana ai contributi recati da Galileo le macchine elettriche. Ferraris alla teoria scientifica del trasfor- Prendendo le mosse da questi ele- matore e all’invenzione del campo ro- menti, verranno ravvisati, lungo il per- tante, si colloca, nel quadro della cultu- corso Mossotti, Codazza, Ferraris, ra e della società del tempo, la figura Ascoli-Arnò e Giorgi-Lori, gli elemen- dello scienziato italiano. Ne emerge, tra- ti portanti della scuola italiana di mite il suo maestro Giovanni Codazza, elettrotecnica. il ruolo decisivo che sulla sua forma- zione ebbero - oltre a Maxwell, Tait, von L’astuzia scozzese: la dynamical Helmholtz ed Heaviside - il maestro di philosophy questi: Fabrizio Ottaviano Mossotti. -
A Collection of Definitions and Fundamentals for a Design-Oriented
A collection of definitions and fundamentals for a design-oriented inductor model 1st Andr´es Vazquez Sieber 2nd M´onica Romero * Departamento de Electronica´ * Departamento de Electronica´ Facultad de Ciencias Exactas, Ingenier´ıa y Agrimensura Facultad de Ciencias Exactas, Ingenier´ıa y Agrimensura Universidad Nacional de Rosario (UNR) Universidad Nacional de Rosario (UNR) ** Grupo Simulacion´ y Control de Sistemas F´ısicos ** Grupo Simulacion´ y Control de Sistemas F´ısicos CIFASIS-CONICET-UNR CIFASIS-CONICET-UNR Rosario, Argentina Rosario, Argentina [email protected] [email protected] Abstract—This paper defines and develops useful concepts related to the several kinds of inductances employed in any com- prehensive design-oriented ferrite-based inductor model, which is required to properly design and control high-frequency operated electronic power converters. It is also shown how to extract the necessary parameters from a ferrite material datasheet in order to get inductor models useful for a wide range of core temperatures and magnetic induction levels. Index Terms—magnetic circuit, ferrite core, major magnetic loop, minor magnetic loop, reversible inductance, amplitude inductance I. INTRODUCTION Errite-core based low-frequency-current biased inductors F are commonly found, for example, in the LC output filter of voltage source inverters (VSI) or step-down DC/DC con- verters. Those inductors have to effectively filter a relatively Fig. 1. General magnetic circuit low-amplitude high-frequency current being superimposed on a relatively large-amplitude low-frequency current. It is of practitioner. A design-oriented inductor model can be based paramount importance to design these inductors in a way that on the core magnetic model described in this paper which a minimum inductance value is always ensured which allows allows to employ the concepts of reversible inductance Lrevˆ , the accurate control and the safe operation of the electronic amplitude inductance La and initial inductance Li, to further power converter. -
Magnetic Properties of Materials Part 1. Introduction to Magnetism
Magnetic properties of materials JJLM, Trinity 2012 Magnetic properties of materials John JL Morton Part 1. Introduction to magnetism 1.1 Origins of magnetism The phenomenon of magnetism was most likely known by many ancient civil- isations, however the first recorded description is from the Greek Thales of Miletus (ca. 585 B.C.) who writes on the attraction of loadstone to iron. By the 12th century, magnetism is being harnessed for navigation in both Europe and China, and experimental treatises are written on the effect in the 13th century. Nevertheless, it is not until much later that adequate explanations for this phenomenon were put forward: in the 18th century, Hans Christian Ørsted made the key discovery that a compass was perturbed by a nearby electrical current. Only a week after hearing about Oersted's experiments, Andr´e-MarieAmp`ere, presented an in-depth description of the phenomenon, including a demonstration that two parallel wires carrying current attract or repel each other depending on the direction of current flow. The effect is now used to the define the unit of current, the amp or ampere, which in turn defines the unit of electric charge, the coulomb. 1.1.1 Amp`ere's Law Magnetism arises from charge in motion, whether at the microscopic level through the motion of electrons in atomic orbitals, or at macroscopic level by passing current through a wire. From the latter case, Amp`ere'sobservation was that the magnetising field H around any conceptual loop in space was equal to the current enclosed by the loop: I I = Hdl (1.1) By symmetry, the magnetising field must be constant if we take concentric circles around a current-carrying wire. -
Apparatus Named After Our Academic Ancestors, III
Digital Kenyon: Research, Scholarship, and Creative Exchange Faculty Publications Physics 2014 Apparatus Named After Our Academic Ancestors, III Tom Greenslade Kenyon College, [email protected] Follow this and additional works at: https://digital.kenyon.edu/physics_publications Part of the Physics Commons Recommended Citation “Apparatus Named After Our Academic Ancestors III”, The Physics Teacher, 52, 360-363 (2014) This Article is brought to you for free and open access by the Physics at Digital Kenyon: Research, Scholarship, and Creative Exchange. It has been accepted for inclusion in Faculty Publications by an authorized administrator of Digital Kenyon: Research, Scholarship, and Creative Exchange. For more information, please contact [email protected]. Apparatus Named After Our Academic Ancestors, III Thomas B. Greenslade Jr. Citation: The Physics Teacher 52, 360 (2014); doi: 10.1119/1.4893092 View online: http://dx.doi.org/10.1119/1.4893092 View Table of Contents: http://scitation.aip.org/content/aapt/journal/tpt/52/6?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Crystal (Xal) radios for learning physics Phys. Teach. 53, 317 (2015); 10.1119/1.4917450 Apparatus Named After Our Academic Ancestors — II Phys. Teach. 49, 28 (2011); 10.1119/1.3527751 Apparatus Named After Our Academic Ancestors — I Phys. Teach. 48, 604 (2010); 10.1119/1.3517028 Physics Northwest: An Academic Alliance Phys. Teach. 45, 421 (2007); 10.1119/1.2783150 From Our Files Phys. Teach. 41, 123 (2003); 10.1119/1.1542054 This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. -
Maxwell Discovers That Light Is Electromagnetic Waves in 1862
MAXWELL DISCOVERS LIGHT IS ELECTROMAGNETIC WAVES James Clerk Maxwell was a Scottish scientist. He worked in the mid-nineteenth century in Scotland and England. At that time, electricity and magnetism had been extensively studied, and it was known since 1831 that electric current produces magnetism. Maxwell added the idea that changing magnetism could produce electricity. The term that Maxwell added to the known equations (called Ampere's law) for magnetism allowed Maxwell to see that there were wave-like solutions, that is, solutions that look like a sine wave (as a function of time). The numbers in Maxwell's equations all came from laboratory experiments on electric- ity and magnetism. There was nothing in those equations about light, and radio waves were completely unknown at the time, so the existence of electromagnetic waves was also completely unknown. But mathematics showed that Maxwell's equations had wave-like solutions. What did that mean? Maxwell proceeded to calculate the speed of those waves, which of course depended on the numbers that came from lab experiments with electricity and magnetism (not with light!). He got the answer 310,740,000 meters per second. Maxwell must have had an \aha moment" when he recognized that number. He did recognize that number: it was the speed of light! He was lecturing at King's College, London, in 1862, and there he presented his result that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He considered this to be more than just a coincidence, and commented: \We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena." 1 2 MAXWELL DISCOVERS LIGHT IS ELECTROMAGNETIC WAVES He published his work in his 1864 paper, A dynamical theory of the electromagnetic field. -
Ee334lect37summaryelectroma
EE334 Electromagnetic Theory I Todd Kaiser Maxwell’s Equations: Maxwell’s equations were developed on experimental evidence and have been found to govern all classical electromagnetic phenomena. They can be written in differential or integral form. r r r Gauss'sLaw ∇ ⋅ D = ρ D ⋅ dS = ρ dv = Q ∫∫ enclosed SV r r r Nomagneticmonopoles ∇ ⋅ B = 0 ∫ B ⋅ dS = 0 S r r ∂B r r ∂ r r Faraday'sLaw ∇× E = − E ⋅ dl = − B ⋅ dS ∫∫S ∂t C ∂t r r r ∂D r r r r ∂ r r Modified Ampere'sLaw ∇× H = J + H ⋅ dl = J ⋅ dS + D ⋅ dS ∫ ∫∫SS ∂t C ∂t where: E = Electric Field Intensity (V/m) D = Electric Flux Density (C/m2) H = Magnetic Field Intensity (A/m) B = Magnetic Flux Density (T) J = Electric Current Density (A/m2) ρ = Electric Charge Density (C/m3) The Continuity Equation for current is consistent with Maxwell’s Equations and the conservation of charge. It can be used to derive Kirchhoff’s Current Law: r ∂ρ ∂ρ r ∇ ⋅ J + = 0 if = 0 ∇ ⋅ J = 0 implies KCL ∂t ∂t Constitutive Relationships: The field intensities and flux densities are related by using the constitutive equations. In general, the permittivity (ε) and the permeability (µ) are tensors (different values in different directions) and are functions of the material. In simple materials they are scalars. r r r r D = ε E ⇒ D = ε rε 0 E r r r r B = µ H ⇒ B = µ r µ0 H where: εr = Relative permittivity ε0 = Vacuum permittivity µr = Relative permeability µ0 = Vacuum permeability Boundary Conditions: At abrupt interfaces between different materials the following conditions hold: r r r r nˆ × (E1 − E2 )= 0 nˆ ⋅(D1 − D2 )= ρ S r r r r r nˆ × ()H1 − H 2 = J S nˆ ⋅ ()B1 − B2 = 0 where: n is the normal vector from region-2 to region-1 Js is the surface current density (A/m) 2 ρs is the surface charge density (C/m ) 1 Electrostatic Fields: When there are no time dependent fields, electric and magnetic fields can exist as independent fields.