Brief History of Gaussian Units
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Chapter 16 – Electrostatics-I
Chapter 16 Electrostatics I Electrostatics – NOT Really Electrodynamics Electric Charge – Some history •Historically people knew of electrostatic effects •Hair attracted to amber rubbed on clothes •People could generate “sparks” •Recorded in ancient Greek history •600 BC Thales of Miletus notes effects •1600 AD - William Gilbert coins Latin term electricus from Greek ηλεκτρον (elektron) – Greek term for Amber •1660 Otto von Guericke – builds electrostatic generator •1675 Robert Boyle – show charge effects work in vacuum •1729 Stephen Gray – discusses insulators and conductors •1730 C. F. du Fay – proposes two types of charges – can cancel •Glass rubbed with silk – glass charged with “vitreous electricity” •Amber rubbed with fur – Amber charged with “resinous electricity” A little more history • 1750 Ben Franklin proposes “vitreous” and “resinous” electricity are the same ‘electricity fluid” under different “pressures” • He labels them “positive” and “negative” electricity • Proposaes “conservation of charge” • June 15 1752(?) Franklin flies kite and “collects” electricity • 1839 Michael Faraday proposes “electricity” is all from two opposite types of “charges” • We call “positive” the charge left on glass rubbed with silk • Today we would say ‘electrons” are rubbed off the glass Torsion Balance • Charles-Augustin de Coulomb - 1777 Used to measure force from electric charges and to measure force from gravity = - - “Hooks law” for fibers (recall F = -kx for springs) General Equation with damping - angle I – moment of inertia C – damping -
On the Covariant Representation of Integral Equations of the Electromagnetic Field
On the covariant representation of integral equations of the electromagnetic field Sergey G. Fedosin PO box 614088, Sviazeva str. 22-79, Perm, Perm Krai, Russia E-mail: [email protected] Gauss integral theorems for electric and magnetic fields, Faraday’s law of electromagnetic induction, magnetic field circulation theorem, theorems on the flux and circulation of vector potential, which are valid in curved spacetime, are presented in a covariant form. Covariant formulas for magnetic and electric fluxes, for electromotive force and circulation of the vector potential are provided. In particular, the electromotive force is expressed by a line integral over a closed curve, while in the integral, in addition to the vortex electric field strength, a determinant of the metric tensor also appears. Similarly, the magnetic flux is expressed by a surface integral from the product of magnetic field induction by the determinant of the metric tensor. A new physical quantity is introduced – the integral scalar potential, the rate of change of which over time determines the flux of vector potential through a closed surface. It is shown that the commonly used four-dimensional Kelvin-Stokes theorem does not allow one to deduce fully the integral laws of the electromagnetic field and in the covariant notation requires the addition of determinant of the metric tensor, besides the validity of the Kelvin-Stokes theorem is limited to the cases when determinant of metric tensor and the contour area are independent from time. This disadvantage is not present in the approach that uses the divergence theorem and equation for the dual electromagnetic field tensor. -
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. -
APPENDICES 206 Appendices
AAPPENDICES 206 Appendices CONTENTS A.1 Units 207-208 A.2 Abbreviations 209 SUMMARY A description is given of the units used in this thesis, and a list of frequently used abbreviations with the corresponding term is given. Units Description of units used in this thesis and conversion factors for A.1 transformation into other units The formulas and properties presented in this thesis are reported in atomic units unless explicitly noted otherwise; the exceptions to this rule are energies, which are most frequently reported in kcal/mol, and distances that are normally reported in Å. In the atomic units system, four frequently used quantities (Planck’s constant h divided by 2! [h], mass of electron [me], electron charge [e], and vacuum permittivity [4!e0]) are set explicitly to 1 in the formulas, making these more simple to read. For instance, the Schrödinger equation for the hydrogen atom is in SI units: È 2 e2 ˘ Í - h —2 - ˙ f = E f (1) ÎÍ 2me 4pe0r ˚˙ In atomic units, it looks like: È 1 1˘ - —2 - f = E f (2) ÎÍ 2 r ˚˙ Before a quantity can be used in the atomic units equations, it has to be transformed from SI units into atomic units; the same is true for the quantities obtained from the equations, which can be transformed from atomic units into SI units. For instance, the solution of equation (2) for the ground state of the hydrogen atom gives an energy of –0.5 atomic units (Hartree), which can be converted into other units quite simply by multiplying with the appropriate conversion factor (see table A.1.1). -
Gauss' Theorem (See History for Rea- Son)
Gauss’ Law Contents 1 Gauss’s law 1 1.1 Qualitative description ......................................... 1 1.2 Equation involving E field ....................................... 1 1.2.1 Integral form ......................................... 1 1.2.2 Differential form ....................................... 2 1.2.3 Equivalence of integral and differential forms ........................ 2 1.3 Equation involving D field ....................................... 2 1.3.1 Free, bound, and total charge ................................. 2 1.3.2 Integral form ......................................... 2 1.3.3 Differential form ....................................... 2 1.4 Equivalence of total and free charge statements ............................ 2 1.5 Equation for linear materials ...................................... 2 1.6 Relation to Coulomb’s law ....................................... 3 1.6.1 Deriving Gauss’s law from Coulomb’s law .......................... 3 1.6.2 Deriving Coulomb’s law from Gauss’s law .......................... 3 1.7 See also ................................................ 3 1.8 Notes ................................................. 3 1.9 References ............................................... 3 1.10 External links ............................................. 3 2 Electric flux 4 2.1 See also ................................................ 4 2.2 References ............................................... 4 2.3 External links ............................................. 4 3 Ampère’s circuital law 5 3.1 Ampère’s original -
Physics, Chapter 30: Magnetic Fields of Currents
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 30: Magnetic Fields of Currents Henry Semat City College of New York Robert Katz University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicskatz Part of the Physics Commons Semat, Henry and Katz, Robert, "Physics, Chapter 30: Magnetic Fields of Currents" (1958). Robert Katz Publications. 151. https://digitalcommons.unl.edu/physicskatz/151 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Robert Katz Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 30 Magnetic Fields of Currents 30-1 Magnetic Field around an Electric Current The first evidence for the existence of a magnetic field around an electric current was observed in 1820 by Hans Christian Oersted (1777-1851). He found that a wire carrying current caused a freely pivoted compass needle B D N rDirection I of current D II. • ~ I I In wire ' \ N I I c , I s c (a) (b) Fig. 30-1 Oersted's experiment. Compass needle is deflected toward the west when the wire CD carrying current is placed above it and the direction of the current is toward the north, from C to D. in its vicinity to be deflected. If the current in a long straight wire is directed from C to D, as shown in Figure 30-1, a compass needle below it, whose initial orientation is shown in dotted lines, will have its north pole deflected to the left and its south pole deflected to the right. -
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. -
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.