Bruker:Phidus/sandkasse-14

• Naturlige enheter
• A. Einstein, The Meaning of Relativity, Princeton University Press, Princeton (1922).
• M, Delmastro, Experimental Particle Physics, CERN School (2022).
• Brazil, Natural units, numbers and numerical clusters, lots of HEP units
• Géraldine Servant, Fundamental Concepts in High Energy Physics, summer student lecture, CERN (2012). Kan brukes som ekstern lenke
• NN, Conversions from HEP to SI
• Florida, HEP units

• Tysk WP, Planck-Einheiten, god på verdier av enheter
• V. Faraoni, Three new roads to the Planck scale, Am. J. Phys. 85, 865–869 (2017).
• DESY, Planck units and QHE
• Kansas, Value atomic units
• Fransk WP, Planck units, hvordan de bygges opp
• Engelsk WP, Stoney units and Planck units with good definitions
• M.J. Duff, L.B. Okun and G. Veneziano, Trialogue on the number of fundamental constants, arXiv:0110060
• F. Wilczek, Units and Magnitudes (lecture notes), very useful. Stored in 2024
• Engelsk WP, Atomic units, very useful

• J.D. Barrow, Natural units before Planck, Quarterly Journal of the Royal Astronomical Society 24, 24–26 (1983).
• APS History, Cavendish and grav constant
• Engelsk WP, Grav constant w/history
• NN, Newton Principia gravitation, stored in 2024
• Engelsk WP, Gaussian grav constant
• Engelsk WP, Planck units
• NN, Grav constant and Planck's natural units
• Blog, All about all natural units
• George Johnstone Stoney med seksjon om Stoney-enheter
• E. Haug, Planck units and G
• Physics Today, Max Planck & natural units
• A. Wutke, From Newton to universal Planck natural units – disentangling the constants of nature, J. Phys. Commun. 7 115001 (2023). Maxwell proposed in 1873 to use units such that G = 1 in Newton grav. law. This meant that mass has units L³T ^-2. Coulombs law then says that mass and charge has same unit. Base units are the same as dimensions?

• Fransk WP, Dimensjon (physique). Innført 1822 av Joseph Fourier hans Theorie analytique de la Chaleur, men han mente eksponentene 3 og - 2 og ikke hele L³T ^-2, i.e. som skaleringsdimensjon!!!
• Karshenboim and Peik, Astrophysics, Clocks and Fundamental Constants, Springer-Verlag, Berlin (2004). Google Book
• M. Melzani, Physique et mesure, Ellipses Éditions, Paris (2022). ISBN 978-2340-068667.
• Joseph Fourier, The Analytical Theory of Heat, Cambridge (1878).
• Måleenhet m/seksjon om naturlige enheter
• Enhetssystem m/seksjon om Heaviside-Lorentz-enheter
• Engelsk WP, Natural Units og Tysk WP spesielt god.
• K.A. Tomilin, Natural Systems of Units, Proceedings 21st International Workshop on the Fundamental Problems of High-Energy Physics and Field Theory, 287-296 (1998). Contains full history
• GNU, Natural units, brukbar innledning
• Wiley, HEP units, stored in 2024
• New Mexico, Unit systems with examples

• Engelsk WP, Atomic units, men mye bedre Fransk WP
• F.L. Pilar, Elementary Quantum Chemistry, Dover Publications, New York (1968). ISBN 0-486-41464-7.
• Text
• G. Johnstone Stoney, On the Physical Units of Nature, Proc. Roy. Dublin Soc. 3, 51–60 (1883).
• Engelsk WP, Dimensionless physical constants
• J.D. Barrow, The Constants of Nature
• J.D. Barrow, Constants of Nature, Youtube video (2003)
• Youtube, Planck units basics

• Unità geometrizzata
• U Penn, Natural units
• Tennessee, Natural and geometrical units

• Ny side
• Nevnes i sammensatte enheter og god svensk WP
• Engelsk WP, Dimensional analysis, innført av Joseph Fourier

• J. Cottingham, Acoustics of free-reed instruments, Physics Today 64 (3), 44 (2011). Stored in 2023
• J. Miller, Physics Today Charles Wheatstone and the English concertina, April (2020). Appeared in Game of Thrones
• Nynorsk WP, Charles Wheatstone, og SNL
• NN, Short and compact bio
• NN, Charles Wheatstone, with bio and nice pictures
• Cambridge U, Collected works with paper to BSA about polar clock
• Popular Science, Polar Clock
• 1902encyclopedia, Charles Wheatstone, good bio plus azimuthal angle in polar clock

• Mexico, Polarized light out of old textbook, w/description of polar clock
• NN, Actual polarization pattern at sunset
• American Cyclopedia, Workings of actual Polar Clock
• Nynorsk WP, Ernst Florens Friedrich Chladni, kanskje lage ny side Ernst Chladni?
• Engelsk WP, Fizeau-Foucault apparatus: In 1834, Charles Wheatstone developed a method of using a rapidly rotating mirror to study transient phenomena, and applied this method to measure the velocity of electricity in a wire and the duration of an electric spark.^[1] He communicated to François Arago the idea that his method could be adapted to a study of the speed of light. Arago expanded upon Wheatstone's concept in an 1838 publication, emphasizing the possibility that a test of the relative speed of light in air versus water could be used to distinguish between the particle and wave theories of light.

In 1845, Arago suggested to Fizeau and Foucault that they attempt to measure the speed of light. Sometime in 1849, however, it appears that the two had a falling out, and they parted ways pursuing separate means of performing this experiment

• Wheatstone 1837, An account of some experiments to measure the velocity of electricity, and the duration of electric light, report to Royal Society

• Kings College, Why Sir Charles Wheatstone should be the new face of the £50 note
• Youtube, Charles Wheatstone and his life, 2020.
• Youtube, Wheatstone Wave Machine, invented late 1840s, this is no. 31 ever made..
• Youtube, The first microphone, Wheatstone realized that sound travelled faster in metal than in air. His microphone used wires instead of pneumatic tubes as in stetoscope. He even planned to send sound through wires and thus invented telephone. Alexander Bell had been student at Kings, as Maxwell was for three years after Maxwell was out of work in Scotland.

• Tysk WP, Charles Wheatstone, med telegrafihistorie om Nadeltelegraf og Zeigertelegraf
• Engelsk WP, Charles Wheatstone, lang og grundig med lenke til Cooke and Wheatstone telegraph
• Nederlandsk WP, Charles Wheatstone kan brukes som mal
• J. Munro, J. Munro, Heros of the Telegraph, The Religious Tract Society, London (1891).
• Russisk WP, Charles Wheatstone, long, detailed with nice figures
• Wheatstone-bro, kan forbedres som nederlandsk WP
• Nature, Wheatstone wave machine, to illustrate polarization
• Encyclopedia Britannica, Sir Charles Wheatstone, England (1911). He measured early how fast electric signal in conductor moved and found close to speed of light. Wheatstone was uncle of Oliver Heaviside
• Paul Drude, Physik der Aether, p. 360 calculates how fast electric signal in conductor moves. On pp 395 calculates wave lengths in Hertz experiment.
• Brian Bowers, Sir Charles Wheatstone FRS: 1802-1875, bare første del, men ser meget bra ut
• S. Ekelöf, The Genesis of the Wheatstone bridge, Engineering Science and Education Journal, February (2001). detailed history, published HERE
• NCIH, Navigation with skylight polarization, vikings and insects
• Kristjansson, History of Iceland Spar
• Blog, Charles Wheatstone bio and HERE and HERE
• SNL, Charles Wheatstone, oppfinner av concertina.
• Engelsk WP, Speed of electricity
• Royal Museum, In 1834 he used a revolving mirror in an experiment to measure the speed of electricity in a conductor. He the then suggested that the same revolving mirror, could be used to measure the speed of light.
• Book, Wheatstone coined word microphone i 1827 and concertina in 1829, men hans mikrofon var virkelig et stetoskop som sagt på [https://de.wikipedia.org/wiki/Charles_Wheatstone tysk WP
• Interesting, Charles Wheatstone and his accomplishment. Also his light speed measurement describes. Also video explaining Cook-Wheatstone telegraph 1839 requiring 5 current lines since have 4 needles in 1839. Then went on to construct the Wheatstone system an automated telegraph system which used a paper tape punched with two rows of holes representing Morse code. This innovative development allowed for an increased transmission of 100 words per minute, as opposed to 10 words per minute. More HERE
• NN, The velocity of electricity and Charles Wheatstone
• Nynorsk WP, Wheatstone-bru og Charles Wheatstone
• Science Museum, Polar Clock 1848 and HERE
• BookDepository, Sir Charles Wheatstone by Brian Bowers
• Youtube, Single Needle Teelegraph, good with history - also HERE
• J. Monroe, Heros of the Telegraph

• Tysk WP, Magnetische Feldkonstante
• Elektrisk konstant

• Kibble-vekt
• Engelsk WP, Kibble balance og på tysk WP som er bedre med refs.

• Engelsk WP, Permittivity
• Italiensk WP, Permittività elettrica, very good, også med grundig frekvensavhengighet for Lorentz-oscillator.
• Kiel U, Frequency dependence, very good
• Dielektrisk materiale, mens dielektrisitetskonstant omdirigeres til permittivitet her.
• SNL, Dielektrikum
• J.A. Fleming, The Principles of Electric Wave Telegraphy, Longmans, Green and Co, London (1910). Permittivity innført av Oliver Heaviside som skulle tilsvare Thomsons magnetiske permeabilitet ifølge engelsk WP.
• NN, Imaginary permittivity and conductivity
• Kiel U, Dynamic permittivity and conductivity, excellent
• F.A. Jenkins and H.White, Fundamentals of Optics, McGraw-Hill, New York (2001). ISBN 0-07-256191-2. Stored in 2023.

• Maxwell, Thomson electrometer, also described in Jenkin book p.100
• Permittivitet eller dielektrisitetskonstant^[2]
• Dielektrisk materiale
• Tysk WP, Permittivität

• E.T. Whittaker, Theories of Aether and Electricity, Wikisource. Excellent on double and Hamiton conical refraction
• MathPages, Whittaker, Einstein and the Aether
• Engelsk WP, A History of Theories of Aether and Electricity
• E.T. Whittaker, A History of the Theories of Aether and Electricity, Chap. 8, Thompson and Maxwell ideas about electric and magnetic properties of aether. Wikisource
• Engelsk WP, Vacuum permittivity, godt skrev et
• P.J. Mohr et al, CODATA recommended values of the fundamental physical constants: 2006, Rev. Mod. Phys. 80, 633-730 (2008). Her blir også elektrisk/magnetisk konstant benyttet
• NIST 2018, vacuum electric permittivity, present value
• PTB, Mitteilungen 2007, her benyttes elektrisk og magnetisk feltkonst
• arXiv, Vacuum permittivity and QED

• Norsk WP, Rayleigh-spredning meget tynn, må rettes opp. Mye bedre nynorsk WP
• Engelsk WP, Rayleigh scattering
• Engelsk WP, Tyndall-effekt, også på nynorsk WP
• B. Holstein, EFT for Rayleigh scattering and much more
• Rayleigh-spredning er elektrisk dipolspredning gitt ved dipolmomentet p. Dette gir riktig vinkel-fordeling som ved Thomson-spredning, man må kun beregne dipolmoment. Dette kan gjøres som for Lorentz-oscillator som Feynman, Wolfram og Fitzpatrick benytter, eller betrakter dielektrisk kule som gjort på Purdue eller i Cornell-forelesningen:
• Cornell, Rayleigh scattering, stored in 2023
• Hyperphysics, Blue Sky, good with Mie Scattering
• Purdue, Rayleigh and Mie scattering, very complete. Stored in 2023
• Feynman, Scattering of light - and blue sky. Also simple HERE
• Fitzpatrick, Rayleigh scattering, derived as by RPF, invoking Thomson x-section
• Youtube, Polarized scattering, clear and with theory
• See also en:Critical Opalescence and in particular Sakurai Adv. QM where also scattering derived in terms of index of refraction.
• Einstein 1910, Critical Opalescence and scattering of light, Ann. Phys.

• Einstein, Rayleigh scattering and critical opalescence
• Indian, Explaining critical opalescence and scattering av light
• New Scientist, Polarization of light from sun, midday horizontally polarized along horizon and when sun set in West, light polarized vertically at the horizon due North and South. All explained in great detail HERE
• NN, Scattering of light in atmosphere, an overview
• G.S. Smith, The polarization of skylight: An example from nature, Am. J. Phys. 75, 25 (2007), calculating polarization in different directions. Stored in 2023. Also read it HERE
• Polarization.net, Polarized Light in Nature and Technology, very many useful webpages with sky polarization patters HERE and explaining Wheatstone polar clock HERE
• Engelsk WP, Rayleigh sky model, polarization of Sun light in great detail
• Blog, Riding to a Polarized Sunset, all clear
• Jstor, Picture of polarization
• Walter Levin Youtube, Lect 30 - Polarizers, Malus' Law, Light Scattering, Blue Skies, Red Sunsets, uten lyd? With red sunset demo. See also HERE for derivation, based on Lorentz model of bound electron.
• Blog, John Tyndall - the man who explained why the sky is blue
• Astroblog, Polar clock well described
• J. Tyndall 1868, Why Blue Sky and Polarized, historically useful and HERE
• Journal, Calculating polarization, celestial coordinates and illustrations. Very useful
• Wolfram, Drude-Lorentz model for index refraction
• Optica, Polarization patterns under different conditions. Spherical angles and planes well explained and HERE
• M. Berry, Babinet and Brewster points in polarization of skylight
• NN, Arago, Babinet and Brewster points due to multiple scattering
• NN, Brief History of Light Polarization
• Lynch and Livingstone and Color and Light in Nature, Cambridge U Press (2001)
• G.P. Können, Polarized Light in Nature, Cambridge University Press, England (1985). ISBN 0-521-25862-6.
• Optics, Polarized skylight with illustration of 90° effect
• Harvard, Scattering and polarization intro
• H.J.J. Winter, The significance of the Bakerian Lecture of 1843
• Youtube, Anti-theft using magnetostriction. More about other systems in English WP
• Marburg, Sky polarization patterns, nice figures p.5
• Forholdet mellom amplitudene for spredt og innkommende lys må være dimensjonsløst. Spredningen skyldes indusert dipolmoment i partikkelen og derfor proporsjonal med dens volum V propto a³ hvor a er radius til partikkelen. Videre må den spredte amplituden avta som 1/r. Derfor har vi at A_s/ A_i propto V/rλ² hvor λ er bølgelengden til lyset. Derfor må den spredte intensitetet gå som I_s propto a⁶/r²λ⁴ som Rayleigh fant.

The three-dimensional celestial hemisphere was represented in two dimensions by a polar-coordinate system, where the zenith angle θ and the azimuth angle φ from West are measured radially and tangentially, respectively. In this two-dimensional coordinate system, the zenith is at the origin and the horizon corresponds to the outermost circle.

Single Rayleigh scattering gives polarization

${\displaystyle P=P_{max}{\sin ^{2}\gamma \over 1+\cos ^{2}\gamma }}$

with cosγ = sinθ_s sinθ cosψ + cosθ_s cosθ where γ is the angular distance between the observed celestial point and the sun, θ_s is the solar zenith angle and θ and ψ are the angular distances of the observed point from the zenith and the solar meridian, respectively.

• For more and illustrations, see English WP Rayleigh sky model

• Youtube, The Wheatstone Bridge, What It Does, and Why It Matters, mer generell beskrivelse
• Youtube, Wheatstone Bridge: A (Not So) Honorable History, historisk bakgrunn

• Engelsk WP, Electrometer
• Nynorsk WP, Elektrometer
• Tysk WP, Spannungswaage, med gode figurer.
• Kibble-vekt må kanskje utvides med litt fysisk innhold?
• Tysk WP, Watt-Waage
• NPL, New kilogram and the watt balance
• J.A. Fleming, Electrometer , Encyclopedia Britannica 1911, great details saying that disk voltmeter goes back to A. Volta.
• Fleeming Jenkin, Electricity and Magnetism, disk electrometer in simplest version pp 100-101
• AIP, Basic Electrostatics with capacitance of spheres/cylinders. Stored in 2023.
• Elektroskop, se også relevant side elektrostatisk induksjon. Tysk WP er god.
• Elektrostatikk inneholder kraft mellom to kondensatorplater som ble brukt i plate-elektrometer, samt Maxwells spenningstensor
• SNL, Elektroskop m/ref til A. Volta
• Nordisk Familjebok, Elektroskop, Runeberg Projekt (1907)
• Youtube, Electroscope & Electrostatic Induction, Nice demo]
• A. Kirillov, Lie groups and Algebras, stored in 2023

• Galvanometer må oppgraderes, konsultér også amperemeter som også mangler refs.
• James Clerk Maxwell, The Scientific Papers of James Clerk Maxwell, Dover Publications, New York (1965). Unabridged version of original published 1895 by Cambridge U. Press
• English WP, Mirror galvanometer
• Bruce J. Hunt on Youtube, Lord Kelvin and telegraphy
• Göttingen, Dreiespolgalvanometer, very good. Also check Thomson speilgalvanometer
• J.A. Fleming, Galvanometer, Encyclopedia Britannica 1911, elementary introduction with history
• Dreiespoleinstrument, godt beskrevet hos O. Øgrim, H. Ormestad og K. Lunde, Rom Stoff, Tid: Fysikk 3FY, bind 3, J.W. Cappelens Forlag, Oslo (1981). ISBN 82-02-01957-5. Også elementær fremstilling hos
• D. Halliday and R. Resnick, Physics, John Wiley & Sons, New York (1986). ISBN 0-471-84513-2 hvor magnetfelt er radielt slik at ingen sinθ- faktor.
• PhD thesis (1916): When a pulse of current passes through a moving coil instrument the coil is given an impulse which sets is swinging. If the duration of the pulse is short compared with the natural period of oscillation of the coil (T), then the amplitude of the oscillation does not depend on the way in which the current varies during the pulse. Such an instrument therefore uses a heavy coil wound on an insulating former giving little or no damping. The mass of the coil gives it a large moment of inertia and therefore makes it swing slowly.
• Fitzpatrick Texas, Galvanometer, basics. Vertical galvanometer described HERE
• SNL, dreiespoleinstrument med mer oppdatert info samt nynorsk WP, elektrisk måleinstrument med ingen utenlandske lenker...
• Engelsk WP, Galvanometer, last section gives theory of tangent galvanometer
• Catalan WP, Galvanometre, has good description of ballistic galvanometer at end
• Nynorsk WP, Ballistisk galvanometer og engelsk WP, ballistic galvanometer
• Russisk WP, Ballistisk galvanometer, very good
• Smith and Wise, Energy and Empire: A Biographical Study of Lord Kelvin, Google Book, not complete
• St. Pius, Function and use of ballistic galvanometer, can also be used to measure capacity - similar to Weber-Kohlrausch?
• Konstanz U, Tangentenbussole med noe historisk forklaring
• India, Damped oscillations of galvanometer from solving diff. equation
• Stackexchange, Damped oscillations of galvanometer
• Boko, Function of ballistic galvanometer and HERE
• NN, Function of ballistic galvanometer, with all equations for derivation som på russisk WP
• NN, EM textbook chapters
• Feynman, AC circuits, Caltech lectures
• K.K. Tewari, Electricity and Magnetism, practical EM

• Kathy, Wheatstone bridge, but also useful info about resistance convoluted history - Jacobi and Siemens brothers.
• Engelsk WP, Charles Wheatstone, in section on Wheatstone Bridge says that he introduced standard for resistance as one foot of copper wire of certain weight
• Nynorsk WP, Charles Wheatstone
• Engelsk WP, Volt, med historie på slutten som forklarer hvordan volt, ohm og farad ble definiert av Comittee of BAAS rundt 1865. Related history well dscribed på English WP, ohm
• Maxwell 1873, A Treatise on Electricity and Magnetism, Wikisource where in Section 768 detailed discussion of different methods to determine his ratio v, i.e. Weber constant = speed of light, which is defined in Section 628
• B.J. Hunt, Imperial Science, Cambridge University Press, England (2022). ISBN 978-1-108-82854-3. VERY USEFUL. Says on p. 170 that the BA standard of resistance (1 ohm) should be 10 million meters per second, i.e. 10⁷ m/s, i.e. 10⁹ cm/s as became final definition, see Elektromagnetisk enhetssystem and as told in IEEE report
• Darrigol, p.68-71 describes first attempt of absolute unit for resistance by Weber ca. 1850 using current in rotating loop acting on magnetic needle. Also how Kirchhoff gave better formulation of Ohm's law.
• Göttingen, Dreiespolgalavanometer
• D.O. Forfar, Maxwell on Physical Standards, great detail on Maxwell-Jenkin paper for the BSA Committee of units.
• ClerkMaxwellFoundation, Maxwell’s contribution to standardising the unit of electrical resistance, more details on Maxwell-Jenkin paper and EMU unit of ohmic resistance, including modern definition based on QHE
• ETHW, Standardization of the Ohm 1861 - 1867, se også mer HER
• Maxwell legacy, Maxwell coil, clearly explained
• Kirk McDonald, Maxwell and relativity, worked-through examples where Maxwell does EM with relative motion. Stored in 2023.
• Leon Rosenfeld, The Velocity of Light and the Evolution of Electrodynamics, Supplemento Nuovo Cimento, (1957). Very interesting about Riemann's mistake in deriving EM wave equation, Herz and much more
• BSA 1873, Reports of the Committee on Electrical Standards, all reports onwards collected in one volume 1873. Jenkin-Maxwell part 1863 is second report, Appendix C:
• Jenkin and Maxwell 1863, On the Elementary Relations between Electrical Measurements, pp 57-96 (1863) with essentially CGS-system with electrostatic and electromagnetic units defined and explained in simplest terms. Denotes ratio emu/esu unit v with value 310 740 000 m/s from Weber-Kohlrausch. Very detailed description of rotating coils for measurement of resistance on pp. 47-48 and in Appendix D, pp. 100-120.
• Maxwell 1873, A Treatise on Electricity and Magnetism, Clarendon Press, Oxford (1873).
• Maxwell 1873, A Treatise on Electricity and Magnetism, Wikisource
• Maxwell 1873, A Treatise on Electricity and Magnetism, tysk utgave. Rotating coil apparatus explained in detail on pp. 510 onwards, i.e. sections 763-766. See also later critical comment and improvement by Rayleigh HERE
• Maxwell 1865, A Dynamical Theory of the Electromagnetic Field, Phil. Trans. Roy. Soc. 155, 459–512 (1865). Modern version HERE
• Maxwell 1868, On a Method of making a Direct Comparison of Electrostatic with Electromagnetic Force; with a Note on the Electromagnetic Theory of Light, Proc. Roy. Soc. 158 (158), 643-657 (1868) finds experimentally speed of light to be 288 000 000 m/s which is 3% lower than Foucault value = 298 000 000 m/s. Contains description of Riemann's wave equation and that of Ludvig Lorenz. Gives details about measurement and detailed derivation of speed related to ε and μ
• IEEE, Resistance unit, history
• Rayleigh and Shuster 1881, Improved experiments to determine unit resistance, or HERE.
• J.J. Thomson 1883, On the Determination of the Number of Electrostatic Units in the Electromagnetic Unit of Electricity, improvement of treatment given by Maxwell in his Treatise on EM, with formulas that are helpful
• Engelsk WP, Fleeming Jenkin, nederlandsk WP er godt utgangspunkt for norsk versjon.
• Fleeming Jenkin, Electricity and Magnetism, Appleton & Co, New York (1873). On pp. 126 onwards clear description of galvanometer and how to measure Earth magnetic field!
• Fleeming Jenkin, Electricity and Magnetism, Appleton & Co, New York (1873). On pp 155-156 simple explanation of resistance from magnet in rotating coil
• Britannica, Fleeming Jenkin, 2009
• EB 1911, Jenkin, Henry Charles Fleeming
• Nature, Obituary, 32, June 18 (1885).
• R.L. Stevenson, Memoir of Fleeming Jenkin, Charles Scribner’s Sons, (1901). Very long and detailed
• Maxwell 1868 experiment to determine c:

He also carried out an experiment to determine the velocity of light. He employed a great resistance coil end of which are to two parallel disks, one of which is moveable. The same difference of potentials which sends the current through the great resistance also causes an attraction between these disks. At the same time, an electric current which, in the actual experiment, was distinct from the primary current, is sent through two coils, fastened, one to the back of the fixed disk, and the other to the back of the moveable disk. The current flows in opposite directions through these coils, so that they repel one another. By adjusting the distance of the two disks the attraction is exactly balanced by the repulsion, while at the same time another observer, by means of a differential galvanometer with shunts, determines the ratio of the primary to the secondary current. Maxwell experimentally determined the number of electrostatic units in an electromagnetic unit and form that he deduced the velocity of light.

• A. Kirillov, Lie groups and Algebras, stored in 2023
• J.D. Jackson, Surface charges on circuit wires and resistors play three roles, American Journal of Physics 64 (7), 855 - (1996). Field is due to surface charges and is need to provide potential and provide confined flow of electric current.
• Stackexchange, Electric field around current-carrying conductor
• NN, Derivation of telegrapher’s equations and field-to-transmission line interaction, modern approach
• Assis et al, The Electric Field Outside a Stationary Resistive Wire Carrying a Constant Current, Foundations of Physics 29, 729-753 (1999). Stored in 2023.
• D. Tong, Lectures on EM - Electrostatics, excellent
• Tong-2, Magnetostatics, stored in 2023
• Tong-3, Electrodynamics, nice derivation of Faraday induction law for moving conductor plus magnetic energy as J⋅A. Stored in 2023
• Tong-4, EM and Relativity, with nice derivation of Maxwell energy-momentum tensor. Stored in 2023
• Tong-5, EM Radiation, with Green's functions and retarded potentials. Stored in 2023
• Tong-6, EM in Matter, stored in 2023

• Youtube, Volta's condenser electrometer explanation or HERE

• Whittaker, Aether and Electricity, p. 202 writes that a velocity c comes up relating electrostatic to electromagnetic units. On p. 232 he writes about Kirchhoff who in 1857 studies electric disturbances along telegraph wires of circular cross-section. Thus he derives telegraph equation. Dropping the diffusive term, this simplifies to wave equation with EM wave velocity c. This was experimentally determined shortly before by Weber and Kohlrausch who found value 3.1 × 10⁸ cm/s.
• Youtube, The Story of the Telegrapher's Equations - from diffusion to a wave., very good HISTORY from Fourier
• Youtube, How the First Transatlantic Submarine Cable in 1858 led to Transmission Line Theory as we know it, Lord Kelvin

• Engelsk WP, Earth-return telegraph, very useful
• Engelsk WP, Electrical telegraph, good history, many figures
• Youtube, Bruce J. Hunt, Thomson and Early Cable History,
• M. Longair, Comments on Maxwell 1865 dynamical paper,
• Engelsk WP, Law of squares
• Atlantic-Cable, Solving Kelvin's equation
• Kirk McDonald, Heaviside and the telegrapher's equation, with some initial history and name given by Poincaré. Stored in 2023.
• Atlantic Cable, Cable History, complete, but very American
• Darrigol in Electrodynamics History p.124 writes that W. Thomson derived his diffusion-like telegraph equation 1854-1855 in letters to G. Stokes. More details in Whittaker pp.228-230. The more complete equation by Heaviside appeared in 1876 without leakage and 1881 with leakage, also by Heaviside.
• Durham, Heaviside and the Telegrapher Equation, very useful. Stored in 2023 and shop how telegrapher eq. can be derived from Maxwell fields outside transmission line instead of using Kirchhoff on a very short piece of the line, shorter than the wavelength considered.
• LibreTexts, Transmission Line Theory, detailed and complete
• B. Hunt, Imperial Science explains importance of telegrapher equation with time constant RC. Here C was measured in electrostatic units m, while R was measured in electromagnetic units m/s which corresponds to ohm. Conversion factor was Weber's constant which at that time corresponded to ungefähr 200 000 km/s. It was for this telegraph problem it was so important to determine a new standard for resistance R.
• B.J. Hunt, Oliver Heaviside: A first-rate oddity, Physics Today 65 (11), 48-54 (2012). Stored in 2023.
• NN, Heaviside bio
• MIT, TEM Transmission Lines, using Maxwell fields around to get telegrapher eq for currents and volts in transmission line. Stored in 2023.
• Japanese, Communication and Poynting vector
• E. Hylleraas, Elektrisitet og Magnetisme, Vol III og i Sommerfeld Elektrodynamik.
• N. Carron, History of electromagnetic units, all you need to know!
• Kansas U, Derivation telegrapher equation
• Surrey, Different electromagnetic unit systems with some history
• Complete history of first Atlantic telegraph cables
• Youtube, How the First Transatlantic Submarine Cable in 1858 led to Transmission Line Theory as we know it, very good about William Thomson (Kelvin) and his (wrong) theory which solved the first cable problem
• Youtube, Transmission Lines: Part 1 An Introduction
• NN video, Telegrapher equation as transmission line
• Engelsk WP, Charles Wheatstone, with history of first telegraphs in UK. Finnes ennå ikke på norsk! Må skrive om Wheatstone-bro som virker ganske rotete.
• Paul J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age, a fantastic book with lots of eqs and pictures, also great details about Kelvin and his calculations.
• NN, More details of Kelvin's understanding of cable properties
• M Longair, Theoretical Concepts in Physics, book in Berlin with excellent chapters on electromagnetism. Got it!
• M Longair, Maxwell's Enduring Legacy: A Scientific History of the Cavendish Laboratory, book in Berlin with excellent chapter on Kelvin's telegraph works. Got it!
• NN, Telegraph cable and Kelvin's contributions. Good Kelvin biography
• Kirk T. McDonald, Distortionless Transmission Line, about Heaviside's contribution and criterion, and why Kelvin's previous approach was not complete since he didn't know about displacement current. Saved in 2022
• ThatsMaths, For Good Comms, Leaky Cables are Best, about the first Atlantic telegraph cables.
• NN, The Telegrapher's Equation, very good and basic numerics and explanations.
• O. Darrigol, Electrodynamics from Ampère to Einstein, Kelvin and Atlantic cable on ppp 124-125. Only available when read on iPad! Book contains everything about electric and magnetic ideas! In connection with cable equation, Kelvin also had to relate electric units to magnetic units which today is trivial detail.

Kelvin considered small piece of cable with resistance per length R and capacitance to ground per length C. Then rate of change of charge on cable element dx is C(∂V/∂t)dx must be equal to the decrease in the current - (∂I/∂x)dx. Then using Ohm's law IR = - ∂V/∂x gives diffusion equation

${\displaystyle RC{\partial V \over \partial t}={\partial ^{2}V \over \partial x^{2}}}$

This is just the Fourier heat equation which Thomson early had failed in love with! Solutions and discussions in Nahin's book about Oliver Heaviside. So when the voltage is turned on at the beginning of the cable, the signal at the end of cable of length l, will rise to a certain fraction of initial value after a time RCl². Doubling the length, signal will take four times longer to reach the end. This is Thomson's law of squares. This allowed him to know the pro properties of long cables from knowledge and experiments of short cables. Much more in following book:

• T.K. Sarkar et al, History of Wireless, thick, green book in Oslo p.237 more details about Heaviside's contribution to telegraph equation which got final form

${\displaystyle RC{\partial V \over \partial t}={\partial ^{2}V \over \partial x^{2}}+LC{\partial ^{2}V \over \partial t^{2}}}$

• Engelsk WP, Loading coil, inductive loading of telegraph lines as proposed by Heaviside

• Norsk WP, ideell linje, med detaljert diskusjon av telegrafligningens konsekvenser. Men klassifisert som uforståelig og uten kontakt til andre språk

• G. Cookson and C.A. Hempstead, A Victorian Scientist and Engineer: Fleeming Jenkin and the Birth of Electrical Engineering, Routledge, New York (2019). ISBN 978-1-1387-0265-3.

• Nature, Obituary, 32, June 18 (1885) med god omtale av hans E&M lærebok
• Engelsk WP, Fleeming Jenkin, nederlandsk WP er godt utgangspunkt for norsk versjon.
• Sjøkabel for kommunikasjon, med litt historie. Kan utvides med refs
• J. Munro, Heros of the Telegraph, The Religious Tract Society, London (1891).
• Fleeming Jenkin, Electricity and Magnetism, Appleton & Co, New York (1873). On pp. 126 onwards clear description of galvanometer and how to measure Earth magnetic field!
• Fleeming Jenkin, Electricity and Magnetism, Appleton & Co, New York (1873). On pp 155-156 simple explanation of resistance from magnet in rotating coil
• Glynde History, Telpher Line: 1885-1890 om hvordan det var tenkt og ble som også HERE
• Engelsk WP, Aerial tramway, telpherage, oder Seilbahn
• Britannica, Fleeming Jenkin, 2009
• EB 1911, Jenkin, Henry Charles Fleeming
• Nature, Obituary, 32, June 18 (1885). Hans bok om E&M blir godt omtalt
• R.L. Stevenson, Memoir of Fleeming Jenkin, Charles Scribner’s Sons, (1901). Very long and detailed

• MKS-systemet
• SNL, Giorgi-systemet

• PTB, Das System der Einheiten, up to date

• IEC, History of the SI
• Italia, Giorgi biography
• Engelsk WP, MKS system of units
• Norsk WP, SI-systemet, språkvask behøves helt i begynnelsen
• Nynorsk WP, MKSA-systemet
• SNL, SI-systemet, god
• SNL, MKSA-systemet
• Engelsk WP, MKS system of units became MKSA in 1946 when CIPM approved ampere A as fourth EM unit in 1939
• Britannica, MKS history and Giorgi
• R.T.G., The Giorgi (M.K.S. 0) System of Units, Nature 133, 597-598 (1934)
• Nature, The Giorgi System of Units, Nature 134, 283 (1934). Very useful
• NN, MKS system history, kort og konsis med god begrunnelse, i.e. overenstemmelse med praktiske størrelser V, A og ohm
• NIST, MKSA and SI system history
• R.B. Goldfarb, Electromagnetic Units, the Giorgi System, and the Revised International System of Units, IEEE Magnetic Letters 9, 1205905 (2018). Much Physik history and equation B = H in vacuum
• Engelsk WP, Giovanni Giorgi
• Italiensk WP, Giovanni Giorgi (fisico)

• Engelsk WP, Giovanni Giorgi
• Istituto Elettrotecnico Nazionale, Giovanni Giorgi verso l’elettrotecnica moderna 1901-2001
• BIPM, History of ampere
• Giovanni Giorgi, Physics Today 11 (2018).
• F. Frezza et al, The Life and Work of Giovanni Giorgi, IEEE Antennas and Propagation Magazine 57 (6), 152-165 (2015).
• Salvo D'Agostino, Giovanni Giorgi, ingegnere elettrotecnico, nel suo tempo, Como (1996) og meget detaljert

• Engelsk WP, MKS system of units became MKSA in 1946 when CIPM approved ampere A as fourth EM unit in 1939
• Engelsk WP, Giovanni Giorgi with good history of MKS -> MKSA. He proposed MKS with additional volt ampere or ohm as fourth EM unit to make better contact with practical applications.
• Tysk WP, Einheitensystem er god, med lenke til nynorsk Einingssystem]. Skriver her Gauss-systemet eller det gaussiske systemet
• Tysk WP, Elektrostatisches Einheitensystem eller ESU
• Tysk WP, Gaussisches Einheitensystem kan benyttes
• Trygve Holtebekk SNL, Enhetssystem, meget bra med litt historie
• SI-systemet og CGS-systemet
• NN, Gaussian units history, very useful in 2022
• S.A. Treese, History and Measurement of the Base and Derived Units, Springer, Cham, Switzerland (2018). ISBN 978-3-319-77576-0. Kindle version for $ 23
• S. D'Agostino , A History of the Ideas of Theoretical Physics, Kluwer Academic Publishers (2000). ISBN 978-1-4020-0244-1. Detailed discussion of Weber-Kohlrausch exp

• S. D'Agostino, Hertz Researches in Theoretical Physics, Centaurus 36, 46-82 (1993). Stored in 2022
• S. D'Agostino, Hertz Researches on Electromagnetic Waves, Hist. Stud. Phys. Sci. 6, 261-323 (1975). Stored in 2022

• Gaussisk målesystem
• Elektrostatisk enhetssystem
• Tysk WP, Gaußsches Einheitensystem, god norm
• Surrey, Unit systems overview, very good
• NN Indians, Hertz and Maxwell equations, historical review supporting Hertz as leading over the Maxwellians. Mentions also Gauss as first proposing EM waves with finite velocity, wave eq written down by Riemann in 1853 without deeper theory (?)
• Salvo D'Agostino, Hertz researches on electromagnetic waves, Hist. Stud. Phys. Sci. 6, 261-323 (1975) discussing Hertz fundamental paper where he reformulated Maxwell equations in vacuum
• R.G. Littlejohn, Gaussian, SI and Other Systems of Units in Electromagnetic Theory, Physics 221A lecture notes, University of California, Berkeley (2020). Stored in 2022.
• L. Kowalski, A short history of the SI units in electricity, The Physics Teacher 24 (32), 97-99 (1986).
• Satellite Nelson, International System of Units, stored in 2022 gives great historical overview
• PhysLibreTexts, The CGS System of Units, clear exposition of Maxwell ems.
• UCSD, Quantum Mechanics and Maxwell ems in CGS Units
• J. Napolitano, SI and CGS Units in Electromagnetism, very clear and also in 2022?
• H. Hertz, Electric Waves, MacMillan and Co, London (1893).

• Kirk McDonald, HOME PAGE, with everything he has done

• Tysk WP, Elektromagnetisches Einheitensystem
• Nature, 150th anniversary of Gauss's first absolute magnetic measurement
• Gauss (1833), Die Intensität der erdmagnetlschen Kraft zürickgeführt auf absolutes Maass, Google Book. Også HER fra Royal Society]
• Potsdam U, Humboldt and Gauss and Erd Magnetismus

• Engelsk WP, HL units eller HL-systemet med også litt om naturlige enheter
• NN, Conversion of HL-units
• Web, EMU - ESU Conversion
• Web, Conversion table
• IUPAC, Conversion SI - ESU - EMU
• D. Petrascheck, Unit system independent formulation of electrodynamics Eur. J. Phys. 42 045201 (2021). Også for KOVARIANT ELEKTRODYNAMIKK. Stored in 2022
• Rice U, Latex math symbols with examples
• Engelsk WP, CGS system with esu and emu units
• Tysk WP, Gaussisches Einheitensystem, med meget god konverteringstabell
• Tysk WP, Elektrostatisches Einheitensystem, med tabell over esu og emu enheter som adskiller seg fra hverandre med potens av c.
• Citizendium, Gaussian units
• BYU, Gaussian units, nice summary, very clear translation of SI Maxwell eqs from SI to gaussian units.
• RPI, Gaussian to SI conversion made simple
• Youtube, Intro gaussian units for magnetostatics
• Youtube, Gaussian Units for EM, very good
• G.D. Garland, The contributions of Carl Friedrich Gauss to geomagnetism, Historia Mathematica 6 (1), 5-29 (1979). Stored in 2022.

• Assis, Weber and Gauss units

• R.T. Birge, On Electric and Magnetic Units and Dimensions, American Journal of Physics 2(2), 41 - 48, (1934). In Dropbox and in D on iPad
• Engelsk WP, CGS system of units, med god seksjon om elektrostatiske enheter
• Engelsk WP, Statcoulomb, clarifying different relations
• Engelsk WP, Statampere
• Tysk WP, Biot = Abampere, men i gaussisk system brukes Statampere. Kun emu enheter for B, H etc
• Jim Napolitano, SI and CGS Units in Electromagnetism, direct calculation of conversion
• R. Clarke, U Surrey, Unit Systems in Electromagnetism, contains it all using my own notation and stored in 2022
• Engineering, ESU and EMU dimensions, stored in 2022
• Engelsk WP, ESU units
• N.J. Carron, Babel of units, arxiv-1506.01951. Excellent where on p.46 he shows why 1 abampere ↔ 10 A
• K.S. Mendelson, On an early proposal for a unified system of units, American Journal of Physics 83, 183-185 (2015). Stored in 2022
• Britannica, Coulomb force
• Goldfarb, Survey of units, very useful

• Tysk WP, Elektromagnetische Masseinheiten. Meget nyttig er omregningstabell på tysk WP CGS Einheiten
• Engelsk WP, Lorentz-Heaviside units, at the end extended to natural HL-units with c = 1.
• N.J. Carron, Babel of units, arxiv-1506.01951. Excellent
• Berkeley, Notes on units
• William Baylis, Electrodynamics: A Modern Geometric Approach, starting up with discussing units and especially natural HL-units with c = 1.
• Revolvy, Conversion between different units

• Youtube, Magnetism, lectures starting from beginnings
• Youtube, Week 1-10 Electrostatic cgs units, CGS units for magnetic fields
• Weber-Kohlrausch, Maxwell
• CGS-systemet, Assis,
• NIST, Electric Units and Standards, (1916)
• PhyLibreTexts, CGS for EM
• A.K.T. Assis et al, Gauss and Weber's Creation of the Absolute System of Units in Physics, 21st Century Science and Technology, 15(3), 40 - 48 (2002). Explains why called absolute system and stored in 2022
• Engineering, ESU and EMU dimensions, stored in 2022
• R. Lanza and A. Meloni, The Earth's Magnetism: An Introduction for Geologists, Springer-Verlag, Berlin (2006). ISBN 3-540-27979-2.
• NIST, Magnetic units
• England, Magnetic units
• A. Trabesinger, Magnetic disunity, Nature Physics,13, 716 (2017).
• Sommerfeld, Electrodynamics, Volume 3. Google Book

• George Johnstone Stoney, med litt om Stoney-enheter som er de første, naturlige enheter. Kanskje best å kalle ny side for Naturlig måleenhet. Veldig god oversikt fra engelsk WP, Natural units og italiensk WP.
• Nature, 150 years with Gaussian units
• Florida U, natural units intro w/examples
• Engelsk WP, cGh units from Gamow etc
• Engelsk WP, Geometrized unit system, G = c = 1.
• Måleenhet med rød lenke til Enhetssystem
• Meterkonvensjonen med en del historie
• W. Weber und R. Kohlrausch, Ueber die Elektricitätsmenge, welche bei galvanischen Strömen durch den Querschnitt der Kette fliesst, Annalen der Physik 99, 10 - 25 (1856). Stored in 2022. Referanse funnet hos K.S. Mendelson, On an early proposal for a unified system of units, American Journal of Physics 83, 183-185 (2015) som gir en meget klar, historisk fremstilling av EM enheter
• Dimensjon kan kanskje suppleres med dimensjonsanalyse?? som på nynorsk WP
• Dansk WP, Måleenhed er ganske god
• Dansk WP, Atomare enheder, 'meget god begrunnelse for Hartree
• Engelsk WP, Natural units, very clear intro
• Engelsk WP, Dimensional analysis, defines difference between dimensions and units
• Frank Wilczek, On Absolute Units III, Physics Today 59(5), 10 (2006).
• Frank Wilczek, On Absolute Units I, 58(10), 12 (2005).
• Frank Wilczek, Fundamental Constants, arXiv:0708.4361 can be used for intro. He refers to Sommerfelds discussion in his Lectures on Theoretical Physics, Volume 3.
• A.K. Tomilin, Natural Systems of Units, Centenary Anniversary of the Planck System. With history
• NN, Dimensions for dummies
• Stanford U, Natural units, Hartree and Planck
• Youtube, Natural units

• Engelsk WP, British Science Association
• Foreningen inspirert av Gesellschaft Deutscher Naturforscher und Ärzte
• BSA festival w/history
• BSA history
• Store årlige møter, science festival med fri afgang for alle.
• B.J. Hunt, The Ohm Is Where the Art Is: British Telegraph Engineers and the Development of Electrical Standards, Osiris 9, 48-63 (1994). Stored in 2022
• P.M.D. Collins, The British Association for the Advancement of Science and Public Attitudes to Science, doktoravhandling, University of Leeds, (1978).
• A.D. Orange, The Origins of the British Association for the Advancement of Science, The British Journal for the History of Science 6 (2), 152-176 (1972). Stored in 2022

• Engelsk WP, Speed of light, says that Paul Drude introduced c notation for speed of light. Samme symbol also used by Weber and Kohlrausch which used this symbol for Weber's constant which is √2⋅c using modern notation. They used for determination the discharge of a Leyden jar.
• Whittaker, Aether and Electricity, p. 202 writes that a velocity c comes up relating electrostatic to electromagnetic units. On p. 232 he writes about Kirchhoff who in 1857 studies electric disturbances along telegraph wires of circular cross-section. Thus he derives telegraph equation. Dropping the diffusive term, this simplifies to wave equation with EM wave velocity c. This was experimentally determined shortly before by Weber and Kohlrausch who found value 3.1 × 10⁸ cm/s.
• Philip Gibbs UCR, Why c for speed of light?, extremely detailed, gives also Drude full credit, but says also that Maxwell himself in his Treatise on EM (1873) at the end discusses Weber's force law for two moving charges, he uses c. Stored in 2022
• Dellinger, NIST, Electric and Magnetic Units, very good overview with historical justifications for Gauss and Heaviside units.
• K.S. Mendelson, On an early proposal for a unified system of units, American Journal of Physics 83, 183-185 (2015). Stored in 2022
• A.K.T. Assis, On the First Electromagnetic Measurement of the velocity of Light by Wilhelm Weber and Rudolf Kohlrausch, in Volta and the History of Electricity, Milano (2003). Stored in 2022
• PhysLibreTexts, Units and Dimensions

Tesla-spole er en spesiell transformator som kan skape høyfrekvente vekselspenninger som kan bli opptil mange hundre kilovolt og med frekvenser som er typisk mellom 50 - 500 kHz. Dette elektriske apparatet ble oppfunnet av Nikola Tesla og patentert 1891.

I motsetning til en vanlig transformator med jernkjerne, er den viktigste delen av dette apparatet to spoler som er svakt koblet til hverandre gjennom åpen luft. De to spolene utgjør en primær og sekundær svingekrets som bringes til resonans ved den induktive koblingen. Det er denne effekten som gir de høye spenningene.

Da Tesla konstruerte de første utgavene av dette apparatet, var hensikten å kunne overføre energi trådløst via elektromagnetiske bølger. Men det viste seg snart også å være velegnet for å lage kunstige lyn og ble forsøkt brukt i forskjellige, medisinske sammenhenger. De første røntgenrørene krevde også høye spenninger som ofte ble skapt av Tesla-spoler.^[3]

Den viktigste anvendelsen fikk likevel Tesla-spolen i utviklingen av de første radioer da dens elektromagnetiske svingninger har frekvenser som tilsvarer radiobølger. Disse kan på dette vis lettere genereres og med mindre båndbredde enn de første gnistsenderne til Guglielmo Marconi hadde. Det tok derfor ikke lang tid før Marconi og andre benyttet seg av de samme idéene som Tesla hadde gjort bruk av i sin spesielle transformator. Dette teknologiske fremskrittet resulterte derfor i juridiske stridigheter rundt patentrettigheter som varte i mange år.^[4]

I dag brukes Tesla-spoler mest i undervisning og ofte som underholdning hvor kraftige, elektriske utladninger skapes på spektakulært vis.

• Youtube, Tesla Coil Physics: How they work or Kathy HERE

• Tesla-spole og Ruhmkorff-spole

• P.F. Dahl, Nuclear Physics Origins writes that Tuve used Tesla coil in his first high-energy accelerator

Teslaspolens prinsipp likner på en forsøksanordning brukt 1886 av Henrich Hertz for å påvise elektromagnetiske bølgers eksistens.

• Youtube, How Does a Tesla Coil Work? A Historical Deep Dive by energetic woman, involving Fizeau as originator
• Dansk WP, Tesla-transformator, med god forklaring av virkemåte
• Youtube, How a Tesla Coil Works
• Tesla-spole og transformator - som er meget grundig!
• Engelsk WP, Tesla coil
• Svensk WP, Teslaspole, flere gode figurer
• Engelsk WP, Resonant inductive coupling used in Tesla coil with nice figures
• Fransk WP, Bobine Tesla eller enda bedre italiansk WP Bobina di Tesla
• PBS, Tesla coil, also used by Rolf Widerø in his first accelerator!
• Nederlandsk WP, Teslaspole, kan brukes som mal?
• NN, Tesla coil is radio transmitter? yes
• NN, Tesla and radio
• Helsinki PhD, Tesla coil thesis, stored in 2022 and in D on iPad
• Paul Nylander, Tesla Coil construction, with formulas
• F.E. Terman, Radio Engineers’ Handbook, McGraw-Hill, New York (1943). Stored in Books on iPad. 1000 pages and contains everything
• J.R. Hallas, Basic Radio: Understanding the Key Building Blocks , Check it Out
• B. Anderson, The Classic Tesla Coil
• Youtube, How vacuum tubes work
• Kathy Youtube, Triode Vacuum Tube: History & Physics #33, very good. Edison effect, laming valve, de Forest fusion w/gas around 19205-06 and then several years later Howard Armstrong who made the triode the central device for all radio by regenerative effect, i.e. positive feedback = tilbakekobling to grid.
• Kathy Youtube, Edwin Howard Armstrong #34, Positive feedback which was Armstrong's first great discovery in 1912, meeting Pupin from Serbia at Columbia University. Armstrong meets Sarnoff in 1914.
• Youtube, How transistors work, basics
• Kathy Youtube, Photoelectric effect #37 and Lenard/Einstein battle
• NN, Armstrong and his oscillator
• Britannica, Edwin H. Armstrong
• Blog, Radio oscillators with vacuum tubes, i.e. Armstrong, Hartley, Colpitt, crystal oscillators

• 
  Nikola Tesla i sitt laboratorium
• 
  Teslaspole på Questacon - National Science and Technology Center i Canberra, Australia

• Heinrich Hertz må utvides
• Kirk McDonald, Energy and momentum for time-dependent dipoles, Am. J. Physik. 90(4), 247-248 (2022). Email kirkmcd@princeton.edu. Stored in 2022

• J.A. Fleming, The Principles of Electric Wave Telegraphy, Longmans, Green & Co, London (1906). 1st Edition
• J.A. Fleming, The Principles of Electric Wave Telegraphy and Telephony, Longmans, Green & Co, London (1910). 2nd Edition
• J.A. Fleming, The Principles of Electric Wave Telegraphy and Telephony, Longmans, Green & Co, London (1916). 3rd Edition

• Rollo Appleyard, Pioneers of Electrical Communication, MacMillan and Co., London 1930. Includes nice bios of Ørsted and Heaviside
• R. Appleyard, Pioneers of Electrical Communication - Heinrich Rudolf Hertz, Electrical Communication, 6(2), 63-78 (1927). With pictures of original experiments. Very good figure showing Knochcnhauer Spirals which Hertz used first. First used with Leyden jar which is then removed. Most likely just inductive coupling between spirals. Stored in 2022
• Halliday-Resnick, EM textbook. On p. 1077 says that frequency in Hertz' original experiment given by standard formula by capacitance C of spark gap and inductance L of high-voltage coil. These were small so that generated high frequency order of magnitude 100 MHz. Hertz created standing waves by reflections so that he could measure wavelength. Combined with known frequency this gave the velocity, which was close to speed of light. This was the main aim of his experiment. Stored in 2022 and on D in iPad
• Rutgers, Electromagnetics and Antennas, around 1000 pages with calc. details. On p. 779 shows that output effect of transmitter is propto square of ℓ/λ, where ℓ is length of antenna for Hertzian oscillator. Since this oscillates with λ = 1 - 10 m, must make ℓ corresponding large for larger effect. And this was what Marconi realised and did. Stored in 2022 and on D in iPad. Simple Hertz antenna also discussed HERE
• Rutgers lecture HERE says that Hertz dipole oscillator with uniform current distribution describes well experiments with small balls at the ends of antenna which can store charge. When these are taken away, current must go to zero at the ends and we have a half-wave antenna with much greater efficiency. And these describe in fact best Hertz' later experiments with reflection and standing waves. Half-wave antenna is resonant or syntoniøc with applied frequency.
• Hugh G.J. Aitken, Syntony and Spark: The Origins of Radio, Princeton University Press, New Jersey (1985). ISBN 0-691-02392-1. Very good on discussing wavelength and frequency of Hertz' first experiments. Says that external plates or spheres had no effect on emission, i.e. did not act like antennas. Mentioned Fizeau who in 1853 shunted a capacitance (Leyden jar) across secondary windings of Rumkorff coil and produced oscillations
• NN, Hertz bio and good description of experiments

• NN, Spark Transmitters, very useful technical description. Stored in 2022
• ETHW, Wireless Telegraphy, detailed histories
• Mark Burgess, Zlibrary, all kinds of books
• Radiohistorie, må ryddes opp og utvides
• Engelsk WP, Oliver Lodge, hand his spiritual convictions
• Engelsk WP, Spark-gap transmitter, EXCELLENT og tilsvarer norsk WP Gnistsender
• Engelsk WP, Monopole antenna, i.e. original Marconi antenna
• Belrose, IEEE, Fassenden and Marconi
• TeslaResearch, Spark-gap transmitters
• Youtube, Construction of spark-gap transmitter, explaining all electronic details
• Youtube, Simple spark-gap transmitter demonstration
• Youtube, Who Invented Wireless? Marconi, Lodge or Tesla?, great, historical talk
• Youtube, How does a Tesla coil work?
• Youtube, Secret History of Electricity, excellent history by energetic lady

• RadioHistory, Heterodyne principle,very simply explained

${\displaystyle y(t)=A\sin(2\pi f_{c}t)+{\frac {1}{2}}Am\left[\sin \left(2\pi \left[f_{c}+f_{m}\right]t+\phi \right)+\sin \left(2\pi \left[f_{c}-f_{m}\right]t-\phi \right)\right].\,}$

• Superheterodynmottaker, lang og detaljert, men kan kanskje forbedres?
• SNL, Radioteknikk, lang og god med klare skjema for heterodyne og FM-modulering. Forklarer superheterodynprinsippet
• Engelsk WP, Heterodyne
• Energetic Youtube woman, David Sarnoff, Howard Armstrong & the Superheterodyne Receiver, EXCELLENT Reginald Fessenden invented heterodyne with audible beat frequency, while Howard Armstrong used same principle with higher beat frequency, i.e. IF, for amplification etc
• Stanford, A Nonlinear History of Radio, very good on vacuum tubes
• Edwin H. Armstrong, lang og detaljert
• Youtube, Superheterodyne
• F. Seitz, The Cosmic Inventor: Reginald Aubrey Fessenden (1866-1932), Am. Phil. Soc. 89(6), 1-77 (1999).
• NN, From Spark to Speech, very good radio history including Righi, Poulsen, etc. Fessenden used a Ruhmkorff coil with a spark rate up to 10 kHz by using a phonographic cylinder with microscopic incisions. Modulation was achieved by connecting a carbon microphone in series with the antenna lead. With this setup, he was able to transmit speech over a distance of 1.5km in December 1900. What may have been the first intelligible voice message ever transmitted by radio was, Is it snowing where you are, Mr Thiessen? If it is, telegraph back and let me know. In January 1906 Fessenden briefly established the first two-way transatlantic radiotelegraphy link, between Brant Rock and his station near Machrihanish on the Kintyre peninsula in western Scotland, but communication was sporadic and couldn’t be maintained during daylight hours or the summer months. (At that time, Marconi was also still struggling to establish a reliable LF transatlantic radiotelegraphy service. He only succeeded after the huge 300kW disc discharger stations at Clifden and Glace Bay became operational in October 1907).

• Ewh, Fessenden and the Early History of Radio Science, great details
• NN, The Father of Voice Radio – Reginald Fessenden
• J.V.L. Hogan, The outline of radio: A brief historical review (chapter 1)
• Vintage Radio, Who really didn invent the superheterodyne?
• D.G. Tucker, Origins and Types of Radio Receivers, details about heterodyne principle
• AntiqueRadio, Who Invented the Superheterodyne?, very detailed

• Salomonsen, Valdemar Poulsen
• Valdemar Poulsen og Lyngby Radio
• Dansk WP, Poulsen-buesender
• T. Bjerge, Elektricitet og Magnetisme

• Reginald Fessenden, much more by F. Seitz, The Cosmic Inventor: Reginald Aubrey Fessenden (1866-1932), Am. Phil. Soc. 89(6), 1-77 (1999).
• Youtube, The Poulsen Arc Transmitter

• Gnistsender og Bærebølge
• Engelsk WP, Spark-gap transmitter
• Tysk WP, Löschfunkensender.
• A.L. Kimball, A College Textbook of Physics, Henry Holt & Co, New York (1917). På side 487 forklarer virkning og fordelen med å ha ekstra kondensator for å få enda høyere spenninger
• Encyclopaedia Britannica, Electric Waves, 11th edition, England (1911). Nevner beregning av V. Bjerknes I begynnelsen

• SNL, Gnistsender og coil
• Tysk WP, Kohärer, nyttig
• Marconi, Nobel talk and biography, very interesting
• M. Raboy, The Man Who Networked the World, good review
• M. Raboy, The Man Who Networked the World, Oxford University Press, New York (2016). ISBN 978-0-1993-13587. Stored in Books on iPad.
• K. Beauchamp, History of Telegraphy, Institution of Engineering and Technology, England (2001). ISBN 0-85296-792-6. Stored in Books on iPad.
• G.R.M. Garratt, The Early History of Radio: From Faraday to Marconi, Institution of Engineering and Technology, England (1994). ISBN 0-85296-845-0. Inside story - also good on H. Hertz. Stored in Books on iPad.
• G. Marconi, Wireless Telegraphy, Journal of the Institute of Electrical Engineers 28(139), 273-297 (1899), in Google Book From Gutenberg to the Internet: A Sourcebook on the History of ..., Volume 2
• IEEE, Good history of Hertz experiments
• Youtube, Hertz experiment using Ruhmkorff inductor
• NewWorldEncyclopedia, Marconi biography, pretty detailed
• APS, First Radio Message to Cross the Atlantic from North America, December 2019
• Magne Lein, Trådløs kommunikasjon i hundre år, Hallo-Hallo 51(3), 12-16 (1995). Marconis fortelling om hvordan han utvidet Hertz' sender med ekstra plater til å lage mye sterkere antenne. Også litt senere i samme blad om Tesla som vurderes som den virkelige oppfinner av radioteknikken
• Fransk WP, Bobine de Ruhmkorff
• Engelsk WP, Induction coil
• NN, Marconi story
• Electronics-note, https://www.electronics-notes.com/articles/history/pioneers/guglielmo-marconi-biography.php Marconi story]
• Norsk-Fransk WP, Gnistsender og Ruhmkorff-spole oversatt til norsk
• Dansk WP, Poulsen-sender, forbedret gnistsender
• Radiobølge kan utvides sammen med elektromagnetisk stråling
• Radiohistorie og radio med litt historie om Guglielmo Marconi og Karl Ferdinand Braun m/nobelforedrag HERE. Han sies også å ha oppfunnet krystallapparat

• K.A. Øye, Sørvågen telegrafstasjoner 1914-1978 i tekst og bilder, Norsk Telemuseum, Sørvågen (2015).

• 1914 kunne telegrafbestyrer T. Johannesen flytte inn i nytt telegrafbygg et par hundre meter ovenfor den gamle stasjonen (Veiviser)
• Operasjon Anklet 2. juledag 1941 sprengte radiomasten i Sørvågen (Veiviser)
• forbandt den med øyene Røst (og Værøy ?)
• Tjøme radio som eksempel. Oppdater Kystradiostasjon
• Sørvågen med omtale av radio stasjon og ref til boken Historiske linjer
• Telegrafdirektør Magne Hermod Petersen sentral for etableringen i Sørvågen 1906
• Lokalhistoriewiki, Telegraf, med bilde av telegrafbygning
• T. Rafto, Telegrafverkets Historie: 1855-1955, A.S John Griegs Boktrykkeri, Bergen (1955). Online fra NB
• H.F. Dahl, Hallo - Hallo! Kringkastingen i Norge 1920 - 1940, J.W. Cappelens Forlag A.S, Oslo (1999). ISBN 82-02-18478-9.
• Engelsk WP, Sørvågen, Moskenes har nederlandsk ref til at Italia hadde den første trådløse telegraf
• Tysk info, Sørvågen Radio, fra lofoten-info? Mye brukbart innhold
• Tysk info-x, Med mer deltjert info og bilder, også nevnt Enigma kryptering for Anklet
• Nedlagte norske kystradiostasjoner hvor Sørvågen radiotelegrafstasjon er listet opp uten tekst, skrevet av Jan S. Krogh. Også nevnt som kystradiostasjon med litt info
• Telegrafi og telegrafist, kanskje skrive Trådløs telegrafi som er listet her og på samme nivå som Optisk telegraf? Bedre navn er Radiotelegrafi da trådløs også kan bety optisk etc
• SNL, Telegrafi, mye bra innhold
• SNL, Radiotelegrafi, litt om Sørvågen og skrivet av Finn Lied
• Engelsk WP, Wireless telegraphy, also HERE
• Ta med Lofot-raid i desember 1941 ssom avledning for Måløy-raidet og ødeleggelsen av radimasten pluss pluss
• Jan S. Krogh, Sørvågen Radio, med masses bilder og tekst
• Aftenposten, Teleeventyret startet i Lofoten, 2. mai 2006, hundre år etter oppstarten 1. mail 1906.
• Museum Nord, Sørvågen= Radiosstasjon, engelsk versjon
• Google images, Sørvågen radio
• Teknisk Museum, Sørvågen Radio, brukbart bilde
• Teknisk Museum, Lødingen: Telegrafens Mekka med mye historie
• Lofoten Booking, Sørvågen Radio, med noe detaljer
• Lofoten info, Sørvågen Radio, med et par gamle bilder
• Nordland Arkiv, Sørvågen med radioprogram om området
• Teknisk Museum, Hermod Petersens billedtelegraf med beskrivelse

• Tysk WP, Oliver Lodge
• Engelsk WP, Oliver Lodge
• Encyclopedia Britannica, Sir Oliver Joseph Lodge
• Science mag, Review of Aitken Syntony and Spark, with all the dates on Lodge

• Maxwell, Ether, Encyclopedia Britannica 9th edition (1878)
• George Francis Fitzgerald
• Oliver Heaviside og telegrafligning 1885.
• Oliver Lodge
• Dansk WP, Kohærer, gitt navnet av Lodge i 1894

• Royal Society of Arts
• Royal Society, Oliver Lodge obituary, great in details
• SNL, Oliver Lodge, skrevet av Oyvind G
• AntiqueWireless, Lodge and physics, very good on lightning and electricity
• Ethw, Lodge bio.
• Encyclopedia.com, Sir Oliver Joseph Lodge, mostly about psychic works
• W.P. Jolly, Sir Oliver Lodge, Psychical Researcher and Scientist, review in Physics Today by Buchholz
• C.G. Raia, From Ether Theory to Ether Theology: Oliver Lodge and the Physics of Immortality, J. Hist. Behav. Sci., 43(1), 19–43 (2007).
• NN, Lodge bio with missing pictures. Lodge wrote his first book Elementary Mechanics at age 26.
• Oliver Lodge org, Homepage with talks and new links
• J. Mussell and G. Gooday (eds.), A Pioneer of Connection: Recovering the Life and Work of Oliver Lodge, University of Pittsburgh Press, Pittsburgh (2020). ISBN 0-8229-4595-9. Begynnelsen gir en god oversikt, også hvordan eteren i elektromagnetismen var inngangsport til det hinsidige. Ble gammel og konservativ, mot Einstein og QM.
• Salmonsens konversationsleksikon, Oliver Joseph Lodge, Andre utgave, Project Runeberg
• P. J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age, The Johns Hopkins University Press, Baltimore (1988). ISBN 0-8018-6909-9.
• Hunt, The Maxwellians in Oslo, p.42 writes that it was the Dane L.V. Lorenz in his paper from 1867 where retarded potensials were introduces, published in Phil. Mag. and later picked up by Fitzgerald

• Impedans og harmonisk oscillator
• Svingekrets, oscillator og faseforskyvning

• Svingekrets, oscillator og faseforskyvning
• Tysk WP, Feddersen
• Engelsk WP, LC circuit, med historiske referanser
• Engelsk WP, [https://en.wikisource.org/wiki/1911_Encyclopædia_Britannica/Electric_Waves
• J. Blanchard, The History of Electrical Resonance, Bell System Technical Journal, 20(4), 415–433 (1941).
• A.L. Kimball, A College Textbook of Physics, Henry Holt & Co, New York (1917).
• L.O. Tveita, Sensorteori: Svingingar og bølgjer, forelesninger ved Sjøkrigsskolen (2010).
• Encyclopaedia Britannica, Telegraph, 11th edition, England (1911).
• Encyclopaedia Britannica, Electric Waves, 11th edition, England (1911).
• Encyclopaedia Britannica, Electrokinetics, 11th edition, England (1911).
• Commons, Marconi antennas

Relativitetsteori er utforming av lovene i fysikk på en slik måte at de er i overensstemmelse med relativitetsprinsippet.

Innen fysikken benyttes relativitetsteorien for å beskrive hvordan naturen oppfører seg ved ekstreme hastigheter eller gravitasjonsfelt. Man skiller gjerne mellom den spesielle og den generelle relativitetsteorien. Førstnevnte beskriver forhold som angår observatører som beveger seg i forhold til hverandre, mens sistnevnte egentlig er en teori om gravitasjonskraften.

Relativitetsteorien ble resultatet av et prosjekt innen fysikken på slutten av 1800-tallet som gikk ut på å forene James Maxwells elektromagnetisme og Isaac Newtons mekanikk. I denne prosessen tårnet det seg opp en rekke teoretiske problemer. En løsning som skulle få omfattende ringvirkninger ble publisert i 1905 under tittelen «Zur Elektrodynamik bewegter Körper». Artikkelen kom ut i fysikkjournalen Annalen der Physik, og forfatteren het Albert Einstein. Den generelle relativitetsteorien ble presentert i 1915.

• Relativitetsteori
• J.D. Norton, Origins of Special Relativity
• Viktighet av Fizeau, Doppler og aberrasjon. Shankland article.
• Relativitetsprinsipp
• Relativitetsprinsipp

• Addisjon av hastigheter
• Absolutt bevegelse
• Mathpages, Doppler effect
• Harvard, NR Doppler
• Book, NR Doppler
• Khan, Doppler video
• NN, NR Doppler
• Opentext, NR Doppler, very clear and detailed
• Engelsk WP, Thomas precession. See Los with many figures:
• Engelsk WP, Wigner rotation
• MIT, Lecture
• NN, Lecture
• Caltech, Lecture, best
• Engelsk WP, Velocity addition formula

• Engelsk WP, Aberration, with detailed calculation at very end of water-filled telescope explained with Fresnel drag.
• Engelsk WP, Fizeau experiment and also good discussion of Hoek experiment and different theories
• Norsk WP, Aberrasjon (astronomi) kan utvides.
• R. Ferraro and D.M. Sforza, Arago experiment and introduction of Fresnel ether dragging, history. Stored in 2020. Historical review by Pedersen about water-filled telescope and resulting theories on aberration and refraction is stored in 2020 as Water-filled telescopes Pedersen.
• R. Newburgh, Fresnel Drag and the Principle of Relativity, Isis 65(3), 379-386 (1974). Stored in 2020.
• R. S. Shankland, Conversations with Albert Einstein, Am. J. Phys. 31, 47–57 (1963). Einstein says that Fizeau experiment was most important for SR together with aberration, not so much Michelson-Morley which he took for granted. Plus much more about his views on QM and Bohr. Text can be found here in archive.org
• RPF, QCD lectures 1987-88 by Jim Cline. READ THEM
• AST1010 UiO, Innføring i astronomi, slides fra forelesninger
• J. D. Norton, How did Einstein Discover the Relativity of Simultaneity?, hvordan aberration was solved by Lorentz introducing local time
• In ether frame no problem to describe aberration in wave theory of light. Problem arises in earth rest frame. Without Lorentz local time there would be no aberration observed there.

• J. Kovalevsky and P.K. Seidelmann, Fundamentals of Astrometry, Cambridge University Press, England (2004). ISBN 0-521-64216-7.
• J. Bradley (1729), An account of a new discovered motion of the fixed stars, Philosophical Transactions of the Royal Society, 35, 637–661 (1729).
• E.T. Whittaker, A History of the Theories Aether and Electricity, Longman, Green & Co, London {1910). archive.org online version.
• A. Hirschfeld, Parallax: The Race to Measure the Cosmos, Henry Holt, New York (2001). ISBN 0-8050-7133-4.
• Mathpages, Stellar Aberration, EXCELLENT
• M. von Laue, Die Mitführung des Lichtes durch bewegte Körper nach dem Relativitätsprinzip, Annalen der Physik 23(10), 989–990 (1907).
• H.A. Lorentz, Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern, E.J. Brill, Leiden (1895).

• Engelsk WP, Principle of relativity
• Engelsk WP, Velocity-addition formula, mye bra innhold, also aberration with calculation of α as difference between the two angles. Må skrives på norsk
• Engelsk WP, Luminiferous aether, history
• Engelsk WP, Lorentz ether theory
• Engelsk WP, Light-dragging effects
• Engelsk WP, Partial ether dragging
• Engelsk WP, Fizeau experiment* NN, Ether drift experiments
• K.F. Schaffner, Nineteenth-Century Aether Theories, Pergamon Press, Oxford (1972). Lorentz explanation of refraction/ether drag. Most helpful explanation
• Science Explained, Aberration simply explained
• arXiv, Water telescope history
• arXiv, Aberration and Fizeau experiment
• Engelsk WP, Lorentz ether theory, very comprehensive
• NN, Detailed trigonometry for aberration
• Tysk WP, Fizau Experiment
• Norsk WP, Armand-Hippolyte Fizeau
• Norsk WP, Eter (fysikk) kan utvides.
• Norsk WP, Aberrasjon (astronomi) kan utvides.
• Polsk WP, History SR, good stuff and nice figures.
• NN, Physics Before and After Einstein, detailed history of Lorentz theory etc
• Bain, Aberration and the ether, saved in 2020.
• Mathpages, Fresnel drag and Fizeau experiment
• Darrigol, Einstein, and contributions by Lorentz and Poincare, French
• J.D. Norton, Goodies, with popular stuff about SR and much more.
• Norton, Ether dragging, very illuminating part of SR overview.
• Norton, Einsteinʼs Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies, elementary but very interesting. Stored in 2020 as Einstein Electrodynamics Moving Bodies. Publisert i boken til Janssen og Lerner, The Cambridge Companion to Einstein.
• J.D. Norton, Einstein’s Investigations of Galilean Covariant Electrodynamics prior to 1905, Archive for History of Exact Sciences 59, 45–105 (2004). More mathematical description of waves for aberration, Fizeau and Lorentz local time and corresponding states. Also magnet-conductor problem and non-rel transformation of E and B som i tysk WP. Stored in 2020.
• J. D. Norton, How did Einstein Discover the Relativity of Simultaneity?, hvordan aberration was solved by Lorentz introducing local time.
• M. Janssen and C. Lehner, The Cambridge Companion to Einstein, Cambridge University Press, Cambridge (2014).ISBN 978-0-521-53542-7. Inneholder Nortons artikkel om elektrodynamikk in moving frames.
• Janssen & Stachel, Electrodynamics and Optics in Moving Bodies, with detailed Fresnel dragging. Stored in 2020 as Ether Janssen Stachel
• M. Janssen, Drawing the line between kinematics and dynamics in special relativity, with detailed ref to Janssen & Stachel
• M. Janssen, CV and list of publications up to 2019.
• Tysk WP, Relativitätstheorie
• Independent, :London, Higgs field and Einstein's New Ether, quoting Wilczek book The Lightness of Being: Mass, Ether and the Unification of Forces and Larry Krauss.
• Görgen UiO, Spesiell relativitet

Observation of aberration can be due to Star moving in immobile ether and Earth at rest in ether. Then star light comes in at angle tanα = v/c wrt normal and is refracted by Glass an angle β so that with Snell we have sinα = n sinβ. Thus sinβ = tanβ = sinα/n or β = v/cn.

Other explanation can be that Earth moves through ether and Star lies fixed in ether. Can then observation of Star be the same? In ref frame fixed to Earth, the ether wind is blowing with velocity -v and makes star light come in again at angle tanα = v/c.

IF ether wind is not dragged by Earth, it will blow through Glass with same velocity -v. Downward travel of light in glass a distance L, will now take a time t = L/(c/n) = nL/c. In same time the horizontal displacement of light will be vt = vnL/c corresponding to a refraction angle tanβ' = β'  = vn/c. This is a factor n² bigger than the refraction angle previously found from Snell's law. Fresnel pointed out that effect would be the same if ether wind in glass is reduced by the same factor som that it blows with horizontal speed -v/n² in Glass. Ether wind speed is reduced because it is partially dragged by Earth.

If now in same situation light moved through glass at rest in moving glass frame Σ' in horizontal direction through immobile ether in rest in frame Σ, then it would move against ether wind in same direction with speed

${\displaystyle c'={c \over n}-{v \over n^{2}}}$

where c/n is light velocity in glass when it is at rest wrt ether, i.e. in Σ Light velocity thus in Sigma; when it moves through glass with relative speed v,

${\displaystyle c_{0}=c'+v={c \over n}+v(1-1/n^{2})}$

This is similar to explanation in Nineteenth-Century Aether Theories which again is based upon Lorentz 1901. Consult also Norton and Whittaker Book on Arago experiment and Fresnel explanation.

• Norton, Ether dragging, very illuminating part of SR overview.
• Norton, Einstein prior to 1905, aberration, Fizeau and Lorentz local time and corresponding states. Stored in 2020.
• Tysk WP, Äther med mange gode figurer

• Utled transformasjon av Maxwell. Se på charge i ro i i system S'. I lab system S gir denne opphav til et elektrisk felt pluss et magnetisk felt som er gitt ved Biot-Savart i NR limit. See Feynman lectures.

• Norsk WP, Relativitetsteori
• Norsk WP, Dialogo sopra i due massimi sistemi del mondo
• Engelsk WP, Galilean invariance
• Tysk WP, Relativitätsprinzip, very good including story about Gran Naviglio
• Engelsk WP, Dialogo sopra i due massimi sistemi del mondo, med linker til italiensk og engelsk oversettelse. Catalansk WP har mye tekst og gode figurer.
• Italiensk WP, Il Gran Naviglio, relativitet forklart med skip i konstant hastighet.
• G. Galilei, Dialog over de store to verdenssystemer, Bokklubben (2008). ISBN 978-82-5257-1042. Oversatt av Kristian Østberg.
• Engelsk WP, Paradox of radiation of charged particles in a gravitational field, very good
• R.P. Feynman, The Laws of Induction, The Feynman Lectures on Physics, Volume II, Chapter 17.
• R.P. Feynman, Lorentz Transformations of the Fields, The Feynman Lectures on Physics, Volume II, Chapter 26.
• NN, Faraday Induction Law and Special Relativity, arXiv
• Tong, DAMTP, Intro SR and EM, stored in 2020
• Feynman, LW-potentials
• Liverpool, Advanced LW, from Lorentz-transformation and stored as Relativistic EM Liverpool in Elektrodynamikk
• NN, Relativistisk elektrodynamikk, basert på at vektorpotensial er 4-vektor
• SNL, Relativistisk elektrodynamikk
• Cockroft, Relativistic EM
• God diskusjon av Faradays induksjonslov på engelsk WP. Kan brukes som utgangspunkt for å bringe inn relativitet.
• H. Kragh, lang biografi om Ludvig Lorenz i Ludvig Lorenz Mie-teori i 2020.
• Tysk WP, Lorentzkraft inneholder mye bra om relativ bevegelse

En partikkel med elektrisk ladning q som beveger seg med hastighet u i et område om elektromagnetiske felt E og B vil bli påvirket av Lorentz-kraften

${\displaystyle \mathbf {F} =q(\mathbf {E} +\mathbf {u} \times \mathbf {B} )}$

Den vil påvirke banen til partikkelen på en måte som er bestemt ved Newtons andre lov F = d p/dt der p er dens relativistiske impuls.

Ved å bruke transformasjonsligningene for feltene og hastigheten u kan man vise at Lorentz-kraften i det transformerte systemet vil ha eksakt samme form, det vil si F' = q(E' + u' × B'). Dette uttrykket for den elektromagnetiske kraften er det samme i alle inertialsystem.

• Tysk WP, Elektromagnetische Masseinheiten. Meget nyttig er omregningstabell på tysk WP CGS Einheiten
• Engelsk WP, Lorentz-Heaviside units, at the end extended to natural HL-units with c = 1.
• N.J. Carron, Babel of units, arxiv-1506.01951. Excellent
• Berkeley, Notes on units
• William Baylis, Electrodynamics: A Modern Geometric Approach, starting up with discussing units and especially natural HL-units with c = 1.
• Revolvy, Conversion between different units
• Island, Old Norse for beginners.

• University Physics^[1]
• Boas^[2]
• Goldstein^[3]
• Goldstine^[4]
• Hand^[5]
• H.K. Sørensen, Kædelinjen, Aarhus Universitet (1996).
• Quantum Frontiers, The enigma of Robert Hooke, Caltech Blog.

• Penn State, Introduction to the Electric Power Grid

• Relativistisk utvidelse av Larmors formel
• Engelsk WP, Classical electromagnetism and special relativity
• Engelsk WP, Covariant formulation of classical electromagnetism
• Løs inhomogens bølgeligning a la Jaskson med deltafunksjon som gir retardert tid. Selve Liénard-Wiechert-potensial kan gjøres ved Lorentz-transformasjon av punktladning som egen side.
• Fitzpatrick, U Texas, Lectures on relativistic electrodynamics where LW-potentials derived by Lorentz-transformation.
• B. Riemann, Beitrag zur Elektrodynamik, 1858
• Leinaas FFV, Noether's theorem pluss alt om Joule v/EHH
• N. Miller, Noether's theorems and Bremsstrahlung: A pedagogical introduction to large gauge transformations and classical soft theorems, basics about gauge symmetries, Harvard 2021

• Egen side med NRQED utledning. Plancks konstant faller bort som i Iowa thesis.

• J.D. Jackson and L.B. Okun, Historical roots of gauge invariance, Reviews of Modern Physics 73, 663-680 (2001) gives history of this force together with history of Ampere and Biot forces. Write that Heaviside found Lorentz-force in impressive paper 1889. The modern Lagrangian for charged particle moving in EM field was written down by K. Schwarzschild in 1903 and Larmor in 1900, interacting with retarded potentials, similar work by Larmor in 1900. Darwin in 1920 expands the retarded LW-potentials in powers of t - t ' = r/c to obtain Darwin interaction between two moving charges. Jackson does it in Coulomb-gauge, while Landa-Lifschitz in Lorentz-gauge.
• Iowa PhD, Darwin interaction, in great detail different derivations, reproduce standard derivations, also from QM for Dirac particles. Saved in Elektrodynamikk as Darwin Interaction PhD
• Kirk McDonald, Electromagnetic momentum, stored in 2022
• Kirk McDonald, Antenna force, stored in 2022
• Kirk McDonald, Darwin interaction, saved in Elektrodynamikk as Darwin Interaction KirkMcD. Also explains change of sign when interaction is expressed by momenta instead of velocities.
• Kirk McDonald, EM field momentum
• Kirk McDonald, Forces between moving charges and EM field momentum.
• H. Essén, The Darwin interaction Energy, all explained! Derived in my Landau & Lifshitz Classical Theory of Fields (1962) on pp 190-193. Also in Jackson book. Essential point is to use Coulomb gauge which is only gauge where Coulomb interaction is independent of time. Stored as Darwin interaction.
• H. Essen, Darwin interaction and superconductivity. Gives survey
• NN, Darwin interaction and historical background for Breit-interaction
• Helgaker, UiO, Many-electron interactions
• B. Holstein, Weak Interactions in Nuclei, with dipole-dipole interaction from reducing Dirac current-current interaction.
• T.H. Boyer, Relativistic Mechanics and a Special Role for the Coulomb Potential, more general derivation of Darwin interaction and relativistic forces. Check out important reference about electric and magnetic forces between moving charges:
• L. Page and N.I. Adams, ”Action and Reaction Between Moving Charges,” Am. J. Phys. 13, 141-147 (1945).
• NN, Feynman paradox for forces between moving charges and solution including field momentum. Stored as Feynman paradoxes.
• Dresden PhD, Bound states in scalar QED, Darwin from one-photon exchange in scalar QED
• U.D. Jentschura, Darwin from scalar QED and pionium. arXiv:hep-ph/0111284
• NN, Darwin derived from one-photon exchange confirming Jackson derivation

• Relativistisk utvidelse av Larmors formel
• Engelsk WP, Classical electromagnetism and special relativity
• Engelsk WP, Covariant formulation of classical electromagnetism
• Løs inhomogens bølgeligning a la Jaskson med deltafunksjon som gir retardert tid. Selve Liénard-Wiechert-potensial kan gjøres ved Lorentz-transformasjon av punktladning som egen side.
• Fitzpatrick, U Texas, Lectures on relativistic electrodynamics where LW-potentials derived by Lorentz-transformation.
• Tong, DAMTP, Intro SR and EM
• Feynman, LW-potentials
• Liverpool, Advanced LW, from Lorentz-transformation and stored as Relativistic EM Liverpool in Elektrodynamikk
• NN, Relativistisk elektrodynamikk, basert på at vektorpotensial er 4-vektor
• SNL, Relativistisk elektrodynamikk
• Cockroft, Relativistic EM
• God diskusjon av Faradays induksjonslov på engelsk WP. Kan brukes som utgangspunkt for å bringe inn relativitet.
• H. Kragh, lang biografi om Ludvig Lorenz i Ludvig Lorenz Mie-teori i 2020.
• J.D. Jackson and L.B.. Okun, Historical roots of gauge invariance, Reviews of Modern Physics 73, 663-680 (2001) gives history of this force together with history of Ampere and Biot forces. Write that Heaviside found Lorentz-force in impressive paper 1889. The modern Lagrangian for charged particle moving in EM field was written down by K. Schwarzschild in 1903, interacting with retarded potentials, similar work by Larmor in 1900. Darwin in 1920 expands the retarded potential in powers of t - t ' = r/c   to obtain Darwin interaction between two moving charges.
• Tysk WP, Lorentzkraft inneholder mye bra om relativ bevegelse

• Skriv først side Klassisk feltteori a la Classical field theory

• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). (Notice that this version and page numbering is different than printed version I have.) On p.268-269 writes that in 1845 Gauss wrote to Weber that forces between particles should be transmitted by at finite velocity, but he had been unable to find a mechanism for this.

• Wilhelm Eduard Weber finnes allerede.
• W. Weber, Elektrodynamische Maasbestimmungen, insbesondere über das Prinzip der Erhaltung der Energie, des X. Bandes der Abhandlungen der mathematisch-physischen Klasse der Königl. Sächsischen Gesellschaft der Wissenshaften, Leipzig (1874).
• W. Weber, Elektrodynamische Maasbestimmungen, Abhandlungen der Sächsischen Gesellschaft der Wissenshaften, Leipzig (1874).
• NN, Weber theory for magnetic force. Maxwell and W. Thomson notation for speed of light c was v. Weber called the corresponding quantity in his theory for c. But this is not todays c. To show the difference, write for Weber's quantity C and then C = √2c where c is todays c. Darrigol p.122.
• Assis, Instantaneous Actions at a Distance, writes on p.49 that Weber proposed in 1846 that general Coulomb force between two moving charges.
• Weber's force law had the problem that charge at rest outside closed, steady current loop, would feel magnetic force. That was a problem. Fechner-current: Two fluids moving with same speed in opposite directions as stated in Assistantships p. 87. But Hall-experiment in 1879 showed that only negative charge moved, positive stayed fixed. See Darrigol p. 210 and there around.
• A. O’Rahilly, Electromagnetic Theory: A Critical Examination of Fundamentals, Dover Publications, New York (1965). More that 900 pages in two volumes!!
• O’Rahilly book says p.203 that weber was the first to develop a theory for discrete charges, thus what Lorentz concluded 50 years later. But Weber theory had big difficulties. One positive aspect was that it involved only relative motions between particles, so no need for aether. But in Clausius theory velocity is wrt aether, in rest system of which where Maxwell eqs are valid. First exe indication of discrete charges was electrolysis, experimentally discovered by Faraday and explained by Clausius in 1857. Maxwell was vehemently against such molecular charges, O’Rahilly p.204. It was first after the lecture by Helmholtz in 1881 that the Maxwellians accepted the possibility of molecular charges.
• Riemann had learned EM from Weber and was influenced by Gauss who wanted a mechanical foundation of electrodynamics. Darrigol p.211 writes that Riemann 1861 wrote Lagrangian(?) for two charges

${\displaystyle L={ee' \over r}{\Big (}1+{{\dot {r}}^{2} \over 2c^{2}}{\Big )}}$

In book by O’Rahilly p.181 it is said that Riemann introduced retarded potential in 1858 and published posthumously in 1868.

• O’Rahilly pp 213-214 derives easily LW-potenstail and calculates directly from those modified Clausius interaction.
• Clausius contribution to this around 1877 discussed in Darrigol, p. 214.
• Schwarzschild derivation (1903) shown in Appendix 9, pp 427-428 of Darrigol. Exactly as today!! Also on previous pages Lorentz derivation from 1892.
• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). (Notice that this version and page numbering is different than printed version I have.) On pp. 420-432 is Lorentz' electrodynamics explained in detail based on ether which always is at rest and not dragged with. Lorentz force is derived from Clausius interaction term e(v⋅A - Φ) between electron charge and field as discussed on p.262. This was done in 1877 in order resolve a question which had been brought up by Helmholtz concerning the interaction between current elements. Clausius expression had also advantage that it did not depend on current consisting of two oppositely moving currents as in Weber's theory. Velocity of particle v is measured to ether which is frame where Maxwell eqs are valid. Lorentz assumed also no more instantaneous interaction between electrons, only through exchange of retarded potentals. For dielectrics moving could also derive Fresnel result for Fizeau experiment, and good dispersion result. Dielectrics where made up of microscopic dipoles with one electron extra and one less as in Poisson theory for magnetization. Only problem for Lorentz theory was null result of Michelson-Morley.

• LW-potensial og deretter trang. of fields. Skriv egen side om LW-potensial med Jackson-utledning. Deretter trang. av E og B

• Tysk WP, Elektrodynamik som også finnes på nynorsk. Den tyske er et godt utgangspunkt for elektrodynamikk som oversiktsartikkel. Den engelske siden er omdirigert til Electromagnetism.
• Engelsk WP, Classical electromagnetism and special relativity
• Engelsk WP, Covariant formulation of classical electromagnetism
• Løs inhomogens bølgeligning a la Jaskson med deltafunksjon som gir retardert tid. Selve Liénard-Wiechert-potensial kan gjøres ved Lorentz-transformasjon av punktladning som egen side.
• Tong, DAMTP, Intro SR and EM
• Feynman, LW-potentials
• Liverpool, Advanced LW, from Lorentz-transformation and stored as Relativistic EM Liverpool in Elektrodynamikk
• NN, Relativistisk elektrodynamikk, basert på at vektorpotensial er 4-vektor
• SNL, Relativistisk elektrodynamikk
• Cockroft, Relativistic EM
• God diskusjon av Faradays induksjonslov på engelsk WP. Kan brukes som utgangspunkt for å bringe inn relativitet.
• H. Kragh, lang biografi om Ludvig Lorenz i Ludvig Lorenz Mie-teori i 2020.
• J.D. Jackson and L.B.. Okun, Historical roots of gauge invariance, Reviews of Modern Physics 73, 663-680 (2001) gives history of this force together with history of Ampere and Biot forces. Write that Heaviside found Lorentz-force in impressive paper 1889. The modern Lagrangian for charged particle moving in EM field was written down by K. Schwarzschild in 1903, interacting with retarded potentials, similar work by Larmor in 1900. Darwin in 1920 expands the retarded potential in powers of t - t ' = r/c   to obtain Darwin interaction between two moving charges.
• Tysk WP, Lorentzkraft inneholder mye bra om relativ bevegelse
• Magnet Lab, Gauss and magnetism
• Britannica, Better definition of gauss unit
• Tysk WP, Gauss-enheter

Im Gegensatz zur klassischen Mechanik ist die Elektrodynamik nicht Galilei-invariant. Das bedeutet, wenn man, wie in der klassischen Mechanik, einen absoluten, euklidischen Raum und eine davon unabhängige absolute Zeit annimmt, dann gelten die Maxwellgleichungen nicht in jedem Inertialsystem.

Einfaches Beispiel: Ein mit konstanter Geschwindigkeit fliegendes, geladenes Teilchen ist von einem elektrischen und einem magnetischen Feld umgeben. Ein zweites, mit gleicher Geschwindigkeit fliegendes und gleich geladenes Teilchen erfährt durch das elektrische Feld des ersten Teilchens eine abstoßende Kraft, da sich gleichnamige Ladungen gegenseitig abstoßen; gleichzeitig erfährt es durch dessen Magnetfeld eine anziehende Lorentzkraft, die die Abstoßung teilweise kompensiert. Bei Lichtgeschwindigkeit wäre diese Kompensation vollständig. In dem Inertialsystem, in dem beide Teilchen ruhen, gibt es kein magnetisches Feld und damit keine Lorentzkraft. Dort wirkt nur die abstoßende Coulombkraft, so dass das Teilchen stärker beschleunigt wird als im ursprünglichen Bezugssystem, in dem sich beide Ladungen bewegen. Dies widerspricht der newtonschen Physik, bei der die Beschleunigung nicht vom Bezugssystem abhängt.

Diese Erkenntnis führte zunächst zu der Annahme, dass es in der Elektrodynamik ein bevorzugtes Bezugssystem gäbe (Äthersystem). Versuche, die Geschwindigkeit der Erde gegen den Äther zu messen, schlugen jedoch fehl, so zum Beispiel das Michelson-Morley-Experiment. Hendrik Antoon Lorentz löste dieses Problem mit einer modifizierten Äthertheorie (Lorentzsche Äthertheorie), die jedoch von Albert Einstein mit seiner speziellen Relativitätstheorie abgelöst wurde. Einstein ersetzte Newtons absoluten Raum und absolute Zeit durch eine vierdimensionale Raumzeit. In der Relativitätstheorie tritt an die Stelle der Galilei-Invarianz die Lorentz-Invarianz, die von der Elektrodynamik erfüllt wird.

In der Tat lässt sich die Verringerung der Beschleunigung und damit die magnetische Kraft im obigen Beispiel als Folge der Längenkontraktion und Zeitdilatation erklären, wenn man die im bewegten System gemachten Beobachtungen in ein ruhendes System zurücktransformiert. In gewisser Weise lässt sich daher die Existenz von magnetischen Phänomenen letztlich auf die Struktur von Raum und Zeit zurückführen, wie sie in der Relativitätstheorie beschrieben wird. Unter diesem Gesichtspunkt erscheint auch die Struktur der Grundgleichungen für statische Magnetfelder mit ihren Kreuzprodukten weniger verwunderlich.

• Larmors formula, dobbelbrytning, transformasjon av EM-felt, først in SR ved koordinatderivasjon, så i kovariant teori ved Lorentz-trans a la RPF.
• Bolvan, Multipoles for Multipolutvikling

• Italiensk WP, Equazione di Larmor eller spansk, gives derivation from Lienard-Wiechert for non-rel motion and also relativistic formula.
• NN, Larmor formula, i.e. non-rel derived in similar way to Richtmyer & Kennard, p 62-63. Stored in 2020.
• D. Schroeder, Purcell simplified, based on E.M. Purcell, Electricity and Magnetism, Stored in 2020.
• D. Schroeder, Larmor formula, excellent. Stored in 2020. Also nice derivation of Rayleigh scattering
• NRAO, Thomsons forenklede utledning av Larmors formel done in 1903, while Larmor presented more obtuse derivation in 1898.
• Erlangen, Thomson derivation of Larmor formula. Stored in 2020.
• LSU, EM radiation a la Jackson with Rayleigh-scattering and diffraction. Stored in 2020.
• R. Fitzpatrick, UT Austin, Thomson-spredning

• Richtmyer and Kennard, p. 461 for direct, simplified derivation with polarisation

• Norsk WP, Krystallmottaker
• Early US radio history
• Early telegraphs in US, from Gauss, Steinheil, Morse, Henry
• Engelsk WP, Single-Wire Earth Return
• Wikiwand, Telegraphs and transmission lines
• NN, The Electromagnetic Telegraph, long and detailed, especially about different codes used
• Amateur Radio, Crystal radio basics
• Electronics, Why you need high-ohm ear-piece

• Engelsk WP, Hertzian dipole
• NN, Hertz resonator sender and receiver, with all practical details for demonstration.
• Engelsk WP, Spark-gap transmitter
• Fransk WP, Emitteur a etincells, mye mer detaljert, med brukbare figurer.
• H. Hertz, Electrical Waves, Dover book på Amazon med mye innhold.
• Nederlandsk WP, Dipolantenne
• Fitzpatrick, U Texas, Hertz dipole with matching load
• Cornell, Hertz dipole, part of long lecture series
• Harvard, Some history around first experiments
• Australia, More about Hertz experiment
• NN, More details about Hertz experiment
• NN, Hertz experiment as LC oscillator
• NN, Excellent lectures on EM, on pp 151-154 about electric and magnetic dipole radiation I can use.
• M. Fowler, Hertz experiments
• J.Z. Buchwald, The Creation of Scientific Effects: Heinrich Hertz and Electric Waves, University of Chicago Press, Chicago (1994). ISBN 0-226-07888-4. Much about Hertz, Helmholtz and rivalry with Weber about electrodynamics. Saved in Oslo as Buchwald - Hertz book. Lost it in hard disk crash!
• J.Z. Buchwald, The Creation of Scientific Effects: Heinrich Hertz and Electric Waves, can read Appendix about Helmholtz calculations.
• NN, Pictures from life of Hertz
• MIT, Antenna basics
• Engelsk WP, Dipole antenna, also some discussion of current distribution.
• India, Antennas, lecture 50, difference between Hertzian and dipole antenna.
• India, Antennas, lecture 48, Hertzian dipole has current distribution constant.
• Bombay, More about antennas for different currents
• NN, Current distributions in antennas
• Toronto, Half wave antenna made up of many Hertzian dipoles.
• NN, More about antennas with different current distributions.
• Cornell. Hertz dipole, excellent EM lecture series

• Benytt til utvidelse av Elektromagnetisk stråling og ta med syklotronstråling, i.e. non-rel synkorotronstråling, jfr. SNL, Synkrotronstråling

En elektrisk ladning som beveger seg med konstant hastighet, kan ikke stråle ut noen energi. Det skyldes at man i dette tilfellet alltid kan finne et referansesystem hvor ladningen ligger i ro. Det elektriske feltet vil da avta med avstanden r som 1/r² og det magnetiske feltet er null. For at ladningen skal kunne skape en elektromagnetisk bølge, må den derfor være akselerert. I det mest generelle tilfellet er da hastigheten en vilkårlig funksjon av tiden. Men ved en Fourier-transformasjon kan en slik funksjon oppløses i komponenter som hver tilsvarer en periodisk bevegelse med en viss vinkelfrekvens ω. Det betyr at man skriver strømtettheten som skaper strålingen, som

${\displaystyle \mathbf {J} (\mathbf {r} ,t)=\int _{-\infty }^{\infty }\!{d\omega \over 2\pi }\mathbf {J} (\mathbf {r} ,\omega )e^{-i\omega t}}$

og likedan for de elektromagnetiske feltene. De er alle reelle størrelser slik at J^*(r,t) = J(r,t). Fourier-komponentene må derfor oppfylle betingelsen

${\displaystyle \mathbf {J} ^{*}(\mathbf {r} ,\omega )=\mathbf {J} (\mathbf {r} ,-\omega )}$

og analogt for alle andre Fourier-komponenter.

Maxwell-ligningene er lineære slik at hver Fourier-komponent vil skape felt som variere med den samme frekvensen og dermed kan lettere beregnes. De fullstendige feltene kan så finnes ved den inverse Fourier-transformasjon.^[1]

Fourier-komponentene for det magnetiske vektorpotensialet kan beregnes fra bølgeligningen. Ved å benytte Lorenz-gaugen, er den nå gitt ved

${\displaystyle {\boldsymbol {\nabla }}^{2}\mathbf {A} (\mathbf {r} ,\omega )+k^{2}\mathbf {A} (\mathbf {r} ,\omega )=-\mu _{0}\mathbf {J} (\mathbf {r} ,\omega )}$

hvor bølgetallet k = ω/c. Dette er en inhomogen Helmholtz-ligning som kan løses på standard måte og gir

${\displaystyle \mathbf {A} (\mathbf {r} ,\omega )={\mu _{0} \over 4\pi }\!\int \!d^{3}x'{\frac {\mathbf {J} (\mathbf {r'} ,\omega )}{|\mathbf {r} -\mathbf {r'} |}}e^{ik|\mathbf {r} -\mathbf {r'} |}}$

for vektorpotensialet i punktet r fra punkt r' i strømkilden. For en statisk strømtetthet ω = 0 går dette resultatet over i Biot-Savarts lov.

Strålingsfeltet sprer seg med lysets hastighet ut i alle retninger, og man er vanligvis bare interessert i dette langt borte fra strømkilden. Det tilsvarer at koordinatene til kildepunktet r' alltid er mye mindre enn de som beskriver feltpunktet r. Man kan da med stor nøyaktighet skrive

${\displaystyle |\mathbf {r} -\mathbf {r'} |=r-\mathbf {n} \cdot \mathbf {r'} }$

hvor enhetsvektoren n har samme retning som r. I nevneren beholder man bare den ledende termen r da den andre gir bidrag til strålingsfeltet som avtar som raskere enn 1/r. Dermed blir

${\displaystyle \mathbf {A} (\mathbf {r} ,\omega )={\mu _{0} \over 4\pi r}e^{ikr}\int \!d^{3}x'\mathbf {J} (\mathbf {r'} ,\omega )e^{-i\mathbf {k} \cdot \mathbf {r'} }={\mu _{0} \over 4\pi r}e^{ikr}\mathbf {J} (\mathbf {k} ,\omega )}$

etter å ha innført k = k n. og en tilsvarende, romlig Fourier-transformasjon av strømtettheten. Den tilsvarende Fourier-komponenten B(r,ω) = ∇ × A(r,ω) til magnetfeltet blir nå

${\displaystyle \mathbf {B} (\mathbf {r} ,\omega )={i\mu _{0} \over 4\pi r}e^{ikr}\int \!d^{3}x'\mathbf {k} \times \mathbf {J} (\mathbf {r'} ,\omega )e^{-i\mathbf {k} \cdot \mathbf {r'} }=i\mathbf {k} \times \mathbf {A} (\mathbf {r} ,\omega )}$

etter å ha benyttet at avstanden r er mye større enn bølgelengden λ til strålingen slik at kr >> 1. Herav kan magnetfeltet som funksjon av tiden B(r,t) finnes som en funksjon av strømtettheten J(r,t) ved en invers Fourier-transformasjon.

Det elektriske feltet er generelt gitt ved de elektromagnetiske potensialene som

${\displaystyle \mathbf {E} =-{\boldsymbol {\nabla }}\Phi -{\partial \mathbf {A} \over \partial t}}$

Her kan det skalare potensialet Φ finnes fra Lorenz-betingelsen

${\displaystyle {\boldsymbol {\nabla }}\cdot \mathbf {A} +{1 \over c^{2}}{\partial \Phi \over \partial t}=0.}$

For de tilsvarende Fourier-komponentene har man dermed sammenhengen

${\displaystyle i\omega \Phi (\mathbf {r} ,\omega )=c^{2}{\boldsymbol {\nabla }}\cdot \mathbf {A} (\mathbf {r} ,\omega )=ic^{2}\mathbf {k} \cdot \mathbf {A} (\mathbf {r} ,\omega )}$

Dermed blir

${\displaystyle {\begin{aligned}\mathbf {E} (\mathbf {r} ,\omega )&=-c{\boldsymbol {\nabla }}(\mathbf {n} \cdot \mathbf {A} )+i\omega \mathbf {A} =-ic\mathbf {k} (\mathbf {n} \cdot \mathbf {A} )+ic(\mathbf {n} \cdot \mathbf {k} )\mathbf {A} \\&=-c\,\mathbf {n} \times (i\mathbf {k} \times \mathbf {A} )=c\mathbf {B} (\mathbf {r} ,\omega )\times \mathbf {n} \end{aligned}}}$

etter å ha brukt betingelsen kr >> 1 i det første leddet. Dette viser at det elektriske feltet står vinkelrett både på det magnetiske feltet og utbredelsesretningen n, noe som karakteriserer alle elektromagnetiske bølger i strålingssonen.^[1]

Når både det elektriske og det magnetiske feltet er kjem, kan den utstrålte energien W beregnes fra Poyntings vektor.S = E × H hvor H = B/μ₀ i vakum. Den totale energien som går gjennom en liten romvinkel dΩ i avstand r fra strømkilden, er da

${\displaystyle {dW \over d\Omega }=r^{2}\!\int _{-\infty }^{\infty }\!dt\,\mathbf {n} \cdot \mathbf {S} ={cr^{2} \over \mu _{0}}\!\int _{-\infty }^{\infty }\!dt\,\mathbf {B} ^{2}(\mathbf {r} ,t)}$

Dette integralet er nå gitt ved et tilsvarende integral over Fourier-komponentene

${\displaystyle \int _{-\infty }^{\infty }\!dt\,\mathbf {B} ^{2}(\mathbf {r} ,t)=\int _{-\infty }^{\infty }\!dt\,\int _{-\infty }^{\infty }\!{d\omega \over 2\pi }\int _{-\infty }^{\infty }\!{d\omega ' \over 2\pi }\mathbf {B} (\mathbf {r} ,\omega )\mathbf {B} (\mathbf {r} ,\omega ')e^{-i(\omega +\omega ')t}}$

Her forenkles nå integrasjonen over tiden da den er gitt ved Diracs deltafunksjon. Dermed vil en frekvensintegrasjon gi at ω = - ω slik at man står igjen med

${\displaystyle {\begin{aligned}&\int _{-\infty }^{\infty }\!dt\,\mathbf {B} ^{2}(\mathbf {r} ,t)=\int _{-\infty }^{\infty }\!{d\omega \over 2\pi }\mathbf {B} (\mathbf {r} ,\omega )\cdot \mathbf {B} (\mathbf {r} ,-\omega )\\&=\int _{-\infty }^{\infty }\!{d\omega \over 2\pi }\mathbf {B} (\mathbf {r} ,\omega )\cdot \mathbf {B} ^{*}(\mathbf {r} ,\omega )={1 \over \pi }\int _{0}^{\infty }\!d\omega |\mathbf {B} (\mathbf {r} ,\omega )|^{2}\end{aligned}}}$

På denne måten kan man definere en frekvens og retningsavhengig strålingsintensitet

${\displaystyle {d^{2}P \over d\omega \,d\Omega }={cr^{2} \over \pi \mu _{0}}|\mathbf {B} (\mathbf {r} ,\omega )|^{2}}$

Ved innsettelse av den magnetiske Fourier-komponenten, kommer man dermed frem til resultat

${\displaystyle {d^{2}P \over d\omega \,d\Omega }={1 \over 16\pi ^{3}c\varepsilon _{0}}|\mathbf {k} \times \mathbf {J} (\mathbf {k} ,\omega )|^{2}}$

etter å ha benyttet at cμ₀ = 1/cε₀ fra definisjonen av [[lyshastigheten. Dette er en generell formel som kan benyttes i mange forskjellige situasjoner til å beregne strålingsintensiteten fra en gitt strømfordeling.^[2]

Kan så ble fortsatt med anvendelse på stråling fra Hertz dipol etc som her.^[3][1]

• Lund U, Vector-spherical harmonics, all you need to know. Stored in 2020 as Vector spherical harmonics

• Tysk WP, Elektrodynamikk som også finnes på nynorsk. Den tyske er et godt utgangspunkt for elektrodynamikk som oversiktsartikkel. Den engelske siden er omdirigert til Electromagnetism.
• Engelsk WP, Classical electromagnetism and special relativity
• Engelsk WP, Covariant formulation of classical electromagnetism
• Løs inhomogens bølgeligning a la Jaskson med deltafunksjon som gir retardert tid. Selve Liénard-Wiechert-potensial kan gjøres ved Lorentz-transformasjon av punktladning som egen side.
• Heidelberg, EM Vorlesungen, Maxwell spenningstensor, D og H pent utledet fra P og M
• Tong, DAMTP, Intro SR and EM
• Feynman, LW-potentials
• Liverpool, Advanced LW, from Lorentz-transformation and stored as Relativistic EM Liverpool in Elektrodynamikk
• NN, Relativistisk elektrodynamikk, basert på at vektorpotensial er 4-vektor
• SNL, Relativistisk elektrodynamikk
• Cockroft, Relativistic EM

• Utvid elektromagnetisk felt med:

Det elektromagnetiske feltet kan kvantiseres og dermed forklare eksistensen av fotoner. I denne kombinisjonen av elektromagnetisme og kvantemekanikk som kalles for kvanteelektrodynamikk, er det det elektromagnetiske firepotensialet A_μ som er den dynamiske variable som kvantiseres. Likevel er det blitt vanlig å si at man dermed har «kvantisert det elektromagnetiske feltet» selv om det elektromagnetiske feltet strengt tatt er gitt ved Faraday-tensoren F_μν = ∂_μA_ν - ∂_νA_μ med komponenter som er det elektriske feltet E og magnetiske feltet B. Samtidig er både A_μ og F_μν  felt ut fra den mer matematiske definisjonen av hva et felt er.

• Duke U, EM lectures including relativistic electrodynamics.
• Jackson, Classical Electrodynamics with very direct derivation of LW-potentials, w only using integral over derivative of delta-function. Simple, geometric explanation of this extra factor in Griffiths.
• Fitzpatrick, U Texas, Lectures on relativistic electrodynamics
• MIT, Fields and radiation from moving charges, also relativistic. Stored in Elektrodynamikk as EM radiation MIT

• J.J. Thomson, Electricity and Matter, Charles Scribner's Sons, New York (1904). Digital utgave, archive.org
• Engelsk WP, Larmor formula P = 2q²a²/3c².
• Erlangen, Thomson derivation of Larmor formula. Stored in 2020.
• Best derivation in book by Pollack and Stump. De skriver I forbindelse med stråling at det var Riemann som først fant ret/adv løsninger av bølgeligning, mens det var Ludvig Lorenz som først benyttet de.
• Anupam Garg, Classical Electromagnetism in a Nutshell, nice examples for Electrodynamics
• McGill, EM fields and radiation, says on p. 30 that Purcell argument for simple derivation of Larmor comes originally from J.J. Thomson and can be found in M. Longair's book Theoretical Concepts in Physics, p.174. Gives most compact derivation of Larmor! Saved in Elektrodynamikk as McGill EM lectures. Contains also good stuff about synchrotron radiation.
• Joseph Larmor, On the theory of the magnetic influence on spectra and on the radiation from moving ions, Phil. Mag, Series 5, 44 (271), 503-512 (1897).
• Thomas Johnson, KTH, Larmor formula with applications, nice and part of lecture series.
• Duke U, Larmors formula with simple, relativistic generalisation
• Blog, Purcell derivation, in small steps
• N. Wheeler, Reed, EM radiation, full series stored in Elektrodynamikk
• Ø. Grøn, SNL, Joseph Larmor
• A.-M. Liénard, Champ électrique et magnétique produit par une charge électrique concentrée en un point et animée d’un mouvement quelconque, L’Éclairage Électrique 16, 5, 53, 106 (1898).
• NN. A.-M. Liénard, lang biografi på fransk.
• Liénard, A. Champ électrique et magnétique produit par une charge électrique, Éclairage Électr. 16, 5–14 (1898).
• E.J. Wiechert, Elektrodynamische Elementargesetze Ann. der Phys. 309, 667 (1901)
• NN, Relativistic Larmor formula
• Canada, Relativistic Larmor formula with intermediate steps from covariant expression. Stored in Elektrodynamikk as Relativistic Larmor Formula. Full lecture course here
• S.P. Puri, Classical Electrodynamics which also derives relativistic formula.
• NMR, Larmor formula background, Zeeman-effect
• Mehra & Rechenberg, The Historical Development of Quantum Theory, first beginnings with Einstein and Larmor etc
• J. Larmor, Mathematical and Physical Papers, Volume 2

• Johannes Skaar, Elektromagnetisme, forelesninger for FYS1120. Lagret i WikiWorks som Johannes Skaar - EM.
• Engelsk WP, Covariant formulation of classical electromagnetism with my metric!
• Må dreie seg om partikler koblet til EM
• Historie, med Weber elektrodynamics, eter, Lorentz, etc. Boken til Assis om Webers elektrodynamikk diskuterer også i detalj Darwin interaction og utleder generell kraft mellom to partikler.
• Engelsk WP, Retarded potentials
• Engelsk WP, Liénard–Wiechert potential
• Synkrotronstråling
• Scattering of light
• Heidelberg, Vorlesungen über Elektrodynamik, med bra multipolutvikling på pp 62-64 og mye mer.
• Inneholder også kovariante formulering på slutten, også elektromagnetisk impulstetthet i medium. Lagret som Heidelberg EM.
• Retarderte potensial ble først brukt av FitzGerald som lærte det av Lord Raleighs Theory of Sound. (The Maxwellians, p.42). Was also used by Lorenz earlier. Ans by Riemann even earlier, first kown after his death). See also Feynman lectures, Vol II, 21.1 - 21.13.
• Elektrodynamikk finnes allerede, men som omdirigering til elektromagnetisme. Denne må oppløses og en ny side om elektrodynamikk må skrives om elektrisk ladde partikler i bevegelse.

• Sjekk ut artikler Induktans og elektromagnetisk induksjon.
• H. Kleinert, Lectures on QED, clear about quantisation. In Oslo Physics folder.

• Karoly Simonyi, A Cultural History of Physics, BEAUTIFUL, contains lots of stuff I want to read. Finnes også på tysk som Kulturgeschichte der Physik. Mye kan leses på Amazon fra begynnelsen av boken.
• Engelsk WP, Ampere's force law
• Tysk WP, Amperesches Kraftgesetz
• Russisk WP, Matematisk forbindelse med Grassmann
• CNRS, Fransk historie

• Fitzpatrick, Texas, Magnetic energy
• Fitzpatrick, Texas, Feynman-Wheeler theory
• Helgaker, UiO, Forelesninger, helt på slutten oppgave om vekselvirkningspotensial og liste med vektoranalytiske resultat.
• Students, Writhing and linking numbers

Før oppdagelsene til Ørsted og Ampère var det allminnelig antatt at magnetiske krefter var analoge til elektriske krefter og skyldes magnetiske ladninger. Dette synet forandret seg i stor grad da disse nye eksperimentene viste seg å forbinde magnetisme til elektrisitet.

Ampère teoretiserte nesten med en gang at alle magnetiske krefter skyldes vekselvirkninger mellom elektriske strømmer, og hans videre forskning gikk ut på å finne en fundamental lov som kunne sammenfatte alle aspektene til disse nye fenomenene. Etter flere års arbeid kom han frem til sin magnetiske kraftlov. Den var basert på å betrakte en tynn, elektrisk leder som fører strømmen I , som oppdelt i «strømelement» Id s når hvert slikt element har en differensiell lengde d s. Hans lov ga kraften mellom to slike strømelement under den viktige betingelse at den skulle tilfredsstille Newtons tredje lov om kraft og motkraft. Dette var en lov av samme type som Newtons gravitasjonslov hvor det ikke er noe mellomliggende felt som formidler kraften og dermed karakteriserer den som en fjernvirkningsteori.

• Kansas, Magnetic boundary conditions

mag mat

Før oppdagelsene til Ørsted og Ampère var det allminnelig antatt at magnetiske krefter var analoge til elektriske krefter og skyldes magnetiske ladninger. Dette synet forandret seg i stor grad da disse nye eksperimentene viste seg å forbinde magnetisme til elektrisitet.

Ampère teoretiserte nesten med en gang at alle magnetiske krefter skyldes vekselvirkninger mellom elektriske strømmer, og hans videre forskning gikk ut på å finne en fundamental lov som kunne sammenfatte alle aspektene til disse nye fenomenene.

Etter flere års arbeid kom han frem til sin magnetiske kraftlov. Den var basert på å betrakte en tynn, elektrisk leder som fører strømmen I , som oppdelt i «strømelement» Id s når hvert slikt element har en differensiell lengde d s. Hans lov ga kraften mellom to slike strømelement under den viktige betingelse at den skulle tilfredsstille Newtons tredje lov om kraft og motkraft. Dette var en lov av samme type som Newtons gravitasjonslov hvor det ikke er noe mellomliggende felt som formidler kraften og dermed karakteriserer den som en fjernvirkningsteori.

For to parallelle ledninger i avstand a og som fører henholdsvis strommene I₁ og I₂, blir den gjensidige kraften mellom ledningene over en strekning b gitt ved Ampères formel

• Christine Blondel and B. Wolff, CNRS, History of Ampere's force law, with details about how value of k changed and mail publications of Ampere.
• Christine Blondel and B. Wolff, CNRS, History of Ampere's force law, with details about how value of k changed and mail publications of Ampere. Fransk version.
• Christine Blondel and B. Wolff, CNRS, History of force law
• CNRS, Discussion of different force laws
• U. Surrey, Ampere's force law with examples
• Russisk WP, Ampere's Law, good for relation to Grassmann.
• NN, Ampere and Biot-Savart forces laws and differences.
• U. Lund, Discussion of different force laws, many webpages.
• UIUC, Lectures on transformations of charges and fields
• UIUC, History of Electromagnetism
• NN, Ampere and Biot-Savart forces laws and differences.
• IEEE, Ampere and Grassmann force laws and differences.
• Barbour, Ampere, Grassmann and Weber forces and Mach Principle.
• NN, How to calculate inductance?
• Kjell Prydz, Electrodynamics: The Field-Free Approach: Electrostatics, Magnetism ...
• U. Lund, Discussion of different force laws, many webpages.
• U. Stockholm, Different force laws

Jeg kunne i begynnelsen på magnetostatikk etter Biot-Savarts lov legge til en liten seksjon om B-feltet fra lukket strømsløyfe uttrykt ved skalart potensial gitt ved romvinkel til sløyfen a la RM p.166. Så kunne jeg i Ampères sirkulasjonslov utvide seksjonen om Historie med subseksjon om B-feltet fra lukket sløyfe som benyttes til å gi sirkulasjonsteoremet direkte, a la i boken til Tricker. Han viser også til at Amperes utledning var mye mer komplisert og annerledes, men ekvivalent til dette. Kan nevnes her at han kalte B-feltet fra lukket sløufe for direktrise. Akkurat dette er klart fremstilt i ekstern lenke til C. Blondel and B. Wolff. Se boken til Assis også. Ta med også lenke til vekselvirkningsenergi mellom to strømsløyfer. Også nevn Laplaces kraftlov som omtalt hos Ampère's Force Law: An Obsolete Formula?, Histoire de l'Électricité et du Magnetisme, CNRS, France.

• A.K.T. Assis, Weber's Electrodynamics, Kluwer Academic Publishers, Dordrecht (1994). ISBN 0-792-33137-0
• H. Grassmann, Neue Theorie der Elektrodynamik, Annalen der Physik und Chemie 64 (1), 1-18 (1845).

• C. Blondel and B. Wolff, CNRS, In Search of a Newtonian Law of Electrodynamics (1820-1826), magnetise krefter i et historisk perspektiv.

• C. Blondel and B. Wolff, CNRS, Ohm's law

• Engelsk WP, Klassisk feltteori
• Engelsk WP, Lagrangian field theory
• Engelsk WP, Covariant formulation of classical EM

• Norsk WP, Spenning (mekanikk)
• Norsk WP, Skjærspenning
• Norsk WP, Normalspenninger

In Assis book pp 115-117 it is describes how Ampere's experiment of orthogonal currents in January 1821 gave a result going against his own force law where he believed that constant k = 0, but in agreement with the then Biot-Savarts law. At this moment he thus gave up publishing his memoir and remained silent for the next two years. The correct value k = -1/2 appeared in 1823. d s × r = ?

• Hugues Chabot and Sophie Roux (eds) La mathématisation comme problème, very good story about Biot and Ampere experiments with timeline på franks).

• Russisk WP, Ampere's Law, good for relation to Grassmann.
• Petsche, Hans-Joachim, Graßmann, Birkhäuser, Basel (2006). ISBN 3-7643-7257-5. I Berlin.
• Petsche, Hans-Joachim Hermann Grassmann, på tysk, men kan lese en god del. På side 293 står det at Grassmann i 1845 ga ut sin avhandlingen
• H. Grassmann, 1845, Neue Theorie der Elektrodynamik i forbindelse med sin Ausdehnungslehre
• Am.J. Phys. ^[1]
• R.A.R. Tricker, Early Electrodynamics, Pergamon Press, London (1965). EXCELLENT. Stored as Tricker - Early Electrodynamics also in Dropbox.
• MacTutor, Jean Baptiste Biot, University of St. Andrews, Scotland.

• EB 1911, Jean-Baptiste Biot
• Norsk WP, Biotitt
• Science History Inst, Ballon trip with Gay-Lussac
• Mactutor, Biot bio, detailed
• Tysk WP, Jean-Baptiste Biot, med god beskrivelse av vitenskapelig aktivitet
• Studentersamfundet
• Meteorites, Biot paper
• Report, on meteorites

• God QM beskrivelse på engelsk WP Quantum Vortex
• Orlando, MIT, Flux Quantization and Vortices, part of excellent lecture series on SC in WikiWorks.
• RPF, Discussions of Feynman's derivation

• R.P. Feynman, The Feynman Lectures on Physics, Vol II, Caltech, Pasadena.
• D. K. Ghosh, Magnetic fields, elektromagnetiske forelesninger, Nptel, Bombay.
• Nptel, Electrodynamics and Relativity

• Feynman Feynman derives the interaction energy from - m\cdotB. With this sign he can when find interaction energy between general current distributions. In the same way, he can derive the total, magnetic energy from the induced fields in solenoids.
• U. Surrey, Magnetic energy starting with field in solenoid.
• U. Colorado, Magnetic energy in circuits with many relevant excerises.
• U. Dublin, Energetics of magnets. Including demagnetising fields and thermodynamics. Also derives standard formula with J and A. In Oslo WikiWorks as Dublin magnetic energy.
• Feynman, Sign of magnetic interaction
• Redlands, Magnetic interaction
• Nptel, Induction and Neumann formula in long EM lecture series.
• N.D. Hari Dass, The Principles of Thermodynamics, good on magnetic fields.

• Fitzpatrick, Texas, Magnetized sphere
• NPtel, Magnetic moment of current loop
• Uni?, Magnetostatics, similar
• Taiwan, Very good!

• Blundell, Magnetism, copy of whole book! In Oslo WikiWorks.
• R.G. Brown, Duke, Electrodynamics, excellent
• Caltech, Feynman papers free to download.
• Maxwell Foundation, Home page for museum in Edinburgh. He is buried in Parton in Galloway.
• NN, Maxwell Legacy with discussion of his different contributions.

• Michelle Feynman, About my father, says that in 1975 he played with his PET computer. I was then there that summer!! But was the PET available so early? No, according to myself, I was there in 1975 at Stanford meeting when I met him and Alvarez at the Stanford Electron-Photon Meeting. I was also there the year after. i.e. 1976. Then he had just had his operation and was back from hospital so that I was with him in his bedroom where the PET stood.
• Caltech, Class of '65 Reunion, Caltech, May 2015, i.e. they started 1961 as first class with the Feynman lectures. Lots of pictures, videos and reminiscenses. Feynman oral question: What is temperature on black body out in space at same distance from Sun as Earth? And: If body was surrounded by suns, it would take its temperature. In real situation it receives only a fraction of the energy corresponding to the solid angle the Sun is seen under from body.
• See Physics Today, April 2005 about how the Feynman lectures got started.
• Microsoft, Feynman Tuva Project, with much RPF stuff and videos.
• Michelle Feynman and Chris Sykes, Caltech TED-talk, 2011 with clips from several NOVA interviews, also from last in 1988.
• Tony Hey 2011, Remembering Feynman
• D. Kaiser 2005, Feynman Diagrams History, with is very first Feynman diagram.
• J. Preskill, 2015, Entanglement, anyons and black holes
• J. Preskill 2018, APS talk about Feynman and his physics, also his lack of interest inn effective field theories.
• Forskningsnytt, Robert Langlands og hans matematikk med andre links.
• Mathpages, Does freely falling charges radiate? with reference to Feynman's thoughts.
• Grøn, Freely falling charges

• Sørensen foto fra Grøn: Robert G. Berntsen

• Regi
• Fotogjengen
• SIT
• ARK

• Klubbstyrets hjemmeside

• Reitz-Milford er bra, gir også ∇⋅B = 0 svært direkte.
• Spansk WP inneholder en del figurer og brukbar tekst.
• Grassmann contribution can be found in last section of Tricker book on early electrodynamics in Dropbox.

Siden finnes allerede på magnetfelt. På engelsk WP hvordan Lorentz-kraften gir entydig bestemmelse av B.

• Darrigol, Electrodynamics from Ampere to Einstein, full online version. In WikiWorks.
• MIT, EM energy and forces, excellent and complete, in WikiWorks
• Encyclopedia.com, Maxwell bio, very good and detailed.
• NN, Maxwell vortex model
• IEEE, Maxwell and his equations
• Dyson, Why is Maxwell so hard to understand?
• France, Maxwell's analogies from elasticity and hydrodynamics
• Royal Society, Maxwell ether ideas
• U Texas, Maxwell's electromagnetic vacuum
• U Michigan, Maxwell's Treatise explained, very good summary of Maxwell's Treatise. In WikiWorks.
• MacTutor, The EM field
• Hunt, Pursuing Power and Light: Technology and Physics from James Watt to Albert Einstein
• Google Book, Biographies of Great Physicists
• Lewis Campbell, Maxwell biography, digital version by Sonnet Software.
• Lewis Campbell (1882), Maxwell biography, all 600 pages! Internet Archive.
• R.T. Glazebrook (1896), James Clerk Maxwell and Modern Physics, Internet Archive.
• D.M. Siegel, Innovation in Maxwell's Electromagnetic Theory: Molecular Vortices, Displacement Current, and Light, Cambridge University Press, Cambridge (2003). ISBN 0-521-53329-5.
• O. Darrigol, Electrodynamics from Ampère to Einstein, Oxford University Press, Oxford (2000). ISBN 0-19-850593-0. T
• Christine Blondel and B. Wolff, CNRS, Ampere-Biot history
• D. Fleisch, A Student's Guide to Maxwell's Equation, Cambridge University Press, Cambridge (2008). ISBN 978-0-511-39308-2.
• Russisk WP, Sirkulasjonsteorem, viser hvordan feltet fra Biot-Savart tilfredsstiller Ampere sirkulasjonsteorem.

Det finnes allerede en side om strålingstrykk som lett kan utvides. I tillegg må nevnes lysmølle og radiometer.

• Tysk WP, Strahlungsdruck har refs to originalarbeid av Maxwell og Lebedev.
• ETH, Maxwell tensor and radiation pressure
• NN, Derivations of radiation pressure formula and Am.J. Phys
• IPFS, Oblique infall
• Textbook, Radiation pressure
• R.P. Feynman, Lectures, radiation pressure
• NN, Physics of Comet tails
• MIT, Electric and magnetic forces. Direct derivation of Maxwell stress tensor with examples. In Oslo folder Electrostatics.
• Eline, Radiation transfer, stored in WikiWorks
• Harvard, Radiation transfer
• Max Planck blog, Very detailed derivation of radiation pressure
• Max Planck blog, The Theory of Heat Radiation
• Net troll, Rad. press. discussion
• Kirk McDonald, Maxwell tensor and radiation pressure
• Griffiths, Photon momentum and the AM controversy with my metric and EM conventions.
• M. Mansuripur, Solar Sails, Optical Tweezers, and Other Light-Driven Machines, arXiv:1206.1385. Med enkle forklaringer, Einstein box and AM-controversy.
• M. Mansuripur, Radiation pressure and EM modes in cavity
• M. Mansuripur, Mechanical effects of light on material media
• The Open University, A Particle Model for Light, web forelesning
• LibreTexts, Numerical examples
• Numerical Recipes, Photon pressure, non-normal direction
• Fitzpatrick, Texas, Maxwell energy-momentum tensor with my signs
• ε₀μ₀ 

• Italiensk WP, Polarizzazione magnetica, ypperlig for hva jeg tenker meg.
• Illinois, Magnetism, excellent about bound currents and B and H. In WikiWorks.
• Fitzpartick, Texas, Magnetisation and magnetic charges
• Engelsk WP, Hund's rules
• Bochum, Magnetic moments with Hund's rules
• Hyperphysics, Hysteresis loop
• Norsk WP, Remanens
• Nynorsk WP, Koersitiv feltstyrke

• J.D. Jackson and L.B.. Okun, Historical roots of gauge invariance, Reviews of Modern Physics 73, 663-680 (2001) gives history of this force together with history of Ampere and Biot forces. Write that Heaviside found Lorentz-force in impressive paper 1889. The modern Lagrangian for charged particle moving in EM field was written down by K. Schwarzschild in 1903, interacting with retarded potentials, similar work by Larmor in 1900. Darwin in 1920 expands the retarded potential in powers of t - t ' = r/c to obtain Darwin interaction between two moving charges.
• J. Larsson, Umeå, EM quasistatic approximations, Am. J. Phys. 75, 230 (2007) including Coulomb, Biot-Savart and Darwin. Elegant derivation of Darwin magnetic vector potential A.
• O. Darrigol, Electrodynamics from Ampère to Einstein, can here read sections on Heaviside, Helmholtz, Hertz, etc
• E. Breitenberger, "Magnetic interactions between charged particles", Am. J. Phys. 36 (1968), 505 for more about Biot-Savart not satisfying Newton's 3 law.
• Indian textbook, Magnetism, including cyclotron and Aurora Borealis.
• A.P. French, Magnetic forces as relativistic effect
• Engelsk WP, Darwin Lagrangian, very nice derivation in transverse Coulomb gauge!
• Assis, Ampere-Weber forces vs Maxwell-Lorentz
• NN, History around Eddington-Darwin-Breit interaction
• NN, QED corrections to pionic hydrogen
• Kirk McDonald, Birkeland, Darboux moving around magnetic monopole
• Kirk McDonald, Relativistic forces between moving charges, going back to FitzGerald and Thompson.
• Kirk McDonald, Ampere's hairpin spaceship and EM field momentum.
• Kirk McDonald, Thomson and Hidden Momentum
• Kirk McDonald, Thomson field momentum
• Kirk McDonald, EM field momentum
• Kirk McDonald, Darwin interaction, saved in Elektrodynamikk as Darwin Interaction KirkMcD. Also explains change of sign when interaction is expressed by momenta instead of velocities.
• Kirk McDonald, Forces between moving charges and EM field momentum.
• Kirk McDonald, Ampere or Biot-Savart forces, detailed discuusion.
• Iowa PhD, Darwin interaction, in great detail, many derivations, also from QM. Saved in Elektrodynamikk as Darwin Interaction PhD
• R.A.R. Tricker, Early Electrodynamics, Pergamon Press, London (1965). EXCELLENT. Stored as Tricker - Early Electrodynamics also in Dropbox.
• NN, Particles in EM fields
• MIT, Quasistatic EM, webpages.
• H. Essén, The Darwin interaction Energy, all explained! Derived in my Landau & Lifshitz Classical Theory of Fields (1962) on pp 190-193. Also in Jackson book. Essential point is to use Coulomb gauge which is only gauge where Coulomb interaction is independent of time. Stored as Darwin interaction.
• B. Holstein, Weak Interactions in Nuclei, with dipole-dipole interaction from reducing Dirac current-current interaction.
• T.H. Boyer, Relativistic Mechanics and a Special Role for the Coulomb Potential, more general derivation of Darwin interaction and relativistic forces. Check out important reference about electric and magnetic forces between moving charges:
• L. Page and N.I. Adams, ”Action and Reaction Between Moving Charges,” Am. J. Phys. 13, 141-147 (1945).
• NN, Feynman paradox for forces between moving charges and solution including field momentum. Stored as Feynman paradoxes.
• Engelsk WP, Breit equation with dipole-dipole interaction?
• Engelsk WP sier at Lorentz-kraften ble først funnet av Heaviside. Se boken p. 117 om han:
• P.J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age, The Johns Hopkins University Press, Baltimore (1988). ISBN 0-8018-6909-9.
• Heidelberg, Vorlesungen über Elektrodynamik, med bra multipolutvikling på pp 62-64 og mye mer. On p. 68 nice proof of

${\displaystyle \int d^{3}x\,\mathbf {J} (\mathbf {x} )=0}$

• Inneholder også kovariante formulering på slutten, også elektromagnetisk impulstetthet i medium. Lagret som Heidelberg EM.

Lorentzkraft eller Lorentz-kraft? Syklotron og syklotronfrekvens.

• Britannica, Lorentz force, mens ladningsbærere i kobber er elektroner, er de positive hull i zink.
• J.J. Roche, B and H, the intensity vectors of magnetism: A new approach to resolving a century-old controversy, American Journal of Physics, 68 (5), 438 - 449 (2000).

• Chapter 1, Electric charges and fields
• Chapter 2, Electrostatic potentials
• Chapter 3, Electric currents
• Chapter 4, Moving charges and magnetism
• Chapter 5, Magnetism and matter
• Chapter 6, EM induction
• Chapter 7, Alternating currents
• Chapter 8, EM waves

• For better understanding consult English WP Faraday's paradox.
• MIT, Lenz's law and EM induction

• Engelsk WP, Lorentz ether theory
• H.A. Lorentz, Nobel talk, 1902.
• Stanley Goldberg, The Lorentz Theory of Electrons and Einstein's Theory of Relativity, Am. J. Phys. 37 (10), 982- (1969).
• Kenneth F. Schaffner, The Lorentz Electron Theory of Relativity, Am. J. Phys. 37 (5), 498- (1969).
• NN, Lorentz bio from Holland with history of electron discovery.
• H. Kragh, Ludvig Lorenz, Electromagnetism, and the Theory of Telephone Currents
• Leiden U, Zeeman, Lorentz & the electron, Dutch, but looks good!
• F. Rohrlich, The Theory of the Electron, forklarer godt hva som var nytt i Lorentz' teori.
• Soviet Encyclopedia, Lorentz-Maxwell Equations, with fundamental equations!
• Miller, Abraham and Lorentz electron theories
• Christa Jungnickel and Russell McCormmach, Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, pp 222-227. On pp 155 etc book tells about Boltzmann's attempts at making mechanical models for Maxwell's els, based on liquids or elastic solids. About Lorentz and his works on pp 232 etc.
• Sommerfeld 1919, Atombau und Spektrallinien, pp 312-314 god diskusjon om Fizeau experiment, eter, etc
• Salmonsens konversationsleksikon (Projekt Runeberg), Elektronteori, EXCELLENT med mange nærliggende artikler om elektron, elektromagnetisme etc. Gir et meget godt bilde av fysikkens tilstand for over hundre år side. Alt dette betyr at jeg må skrive om og forbedre siden om elektron.
• NN, Lorentz-Maxwell theory with Maxwell as macroscopic theory average of microscopic theory.
• NN, Excellent lectures on EM, on pp 151-154 about electric and magnetic dipole radiation I can use.
• J. Field, On the derivation of the Lorentz force
• Engelsk WP, Lorentz ether theory, gives very good overview, including contributions of Poincare and Einstein!
• Salvatore Califano, Pathways to Modern Chemical Physics, history of discovery of electron, Geissler tubes, Hitorf, cathode rays, Hertz investigation, E. Goldstein and his canal rays, Helmholtz vortices, Tait, etc
• Stockholm, Bohr - van Leeuwen theorem, is flux repulsion a classical or QM effect? To be published in Am. J. Phys.
• Feynman, Lecture diamagnetism
• MIT, Lenz's law and EM induction

• Etienne Guyon, Jean-Pierre Hulin and Luc Petit, Physical Hydrodynamics, a beautiful book. Chapter 7 on p. 210 and onwards contains everything about connection between vortices and EM.
• Helge Kragh, The Vortex Atom: A Victorian Theory of Everything, in his book Higher Speculations (2008).
• Utrecht PhD thesis, The Vortex Theory of Atoms, in WikiWorks as Vortex Atom Thesis.
• M. Fowler, Early atomic models

Started with Helmholtz 1858 and his work Ringwirbel .... on vortex tubes = Filaments in hydrodynamics of perfect fluids, i.e. incompressible and no viscosity. Was then taken over by W. Thomson, inspired by mathematical works of G. Stokes. Thomson started his investigations end of 1866, after having worked on magnetism since 1856. Tait had translateted Helmholtz's work to English and made demonstration of vortices by producing smoke rings. It was such a demonstration of Wirbelbewegungen that got Thomson excited on January 22, 1867 in Edinburgh, as he wrote to Helmholtz. Thomson presented his new ideas for vortex atoms in a talk in Edinburgh on Feb. 18, 1867. The sodium atom, producing he double, yellow line, could be two such vortex rings linked together in permanence, allowing for translations, vibrations, rotational and irrational motion. (In rotational motion, any infinitely small element turns around an axis of its own, which is not the case in irrotational motion). Helmholtz himself remained cool towards this vortex theory of atoms. But what Maxwell around the time he wrote his first paper on lines of force, found most interesting was that he has pointed out that the lines of fluid motion are arranged according to the same laws as the lines of magnetic force, the path of an electric current corresponding to a line of axes of those particles of the fluid which are in a state of rotation.

Thomson tried also in the coming years to construct vortex model for the ether, the vortex sponge model. Also worked on by FitzGerald. Big problem with all this was explanation of gravitational attraction between masses as given by Newton. Closest came perhaps Carl Anton Bjerknes who showed from early 1870 that two spherical bodies immersed in a incompressible fluid and pulsating in phase, would attract each other with an inverse square law. But this had not so much to do with the original ideas of Thomson and Tait. Final theory of everything vortex ideas for the ether was used by G. Mie in 1911 (p. 117 in H. Kragh, Quantum Generations: A History of Physics in the Twentieth Century, Princeton University Press (1999). See first chapter here.)

• I.V. Lindell, EM evolution, very concise and correct. Beskriver godt utvikling av Webers ideer. In WikiWorks
• Engelsk WP, History of Maxwell's Equations
• G. Holton and S.G. Brush, Physics, the Human Adventure, Rutgers University Press, New Brunswick, New Jersey (2001). ISBN 0-8135-2908-5. pp 370-380 brukbart om Faraday og Maxwells mekaniske teori for EM.
• Stackexchange, How Maxwell found displacement current as explained by Feynman. Excellent and use it in Maxwells forskyvningsstrøm. Tysk utledning av forskyvningsstrøm.
• Stackexchange, Amperes sirkulasjonslov ble døpt av Heaviside fordi ....???
• T. K. Sarkar, Robert Mailloux, Arthur A. Oliner, M. Salazar-Palma, Dipak L. Sengupta, History of Wireless, great details about Maxwell's derivation of his els. Also about systems of units at that time in connection with Maxwell determination of speed of EM waves. Innholdsfortegnelse kan leses på Amazon, meget interessant, men inneholder også unøyaktigheter.
• F.J. Dyson, Why is Maxwell Theory so hard to understand?
• J.J. Roche, B and H, the intensity vectors of magnetism: A new approach to resolving a century-old controversy, American Journal of Physics, 68 (5), 438 - 449 (2000).
• C.N. Yang, The conceptual origins of Maxwell’s equations and gauge theory, Physics Today, November 2014. Explaining Maxwell's mechanical clockworks! Skriver at W. Thomson (Kelvin) innførte magnetisk vector potential in 1851. Men var ikke det Franz Neumann i 1845? Jo, se Stackexchange med full referanse til Neumanns paper Allgemeine Gesetze Der Inducirten Elektrischen Ströme, Ann. d. Physik 143, (1) 31–44, (1846) (January 1, 1846). Se også Whittaker p.270 where he says that W. Thomson introduced A in 1846, based on elastic model for EM, independently of Neumann, Kirchhoff and Weber.
• Much more detailed history of vector potential and gauge invariance in paper by Yang and WU:
• A.C.T Wu and C.N. Yang, EVOLUTION OF THE CONCEPT OF THE VECTOR POTENTIAL IN THE DESCRIPTION OF FUNDAMENTAL INTERACTIONS, Int. J. Mod. Phys. A 21 (16), 3235–3277 (2006). In WikiWorks as Maxwell - WuYang. Also history of p - eA term in QM and coupling v⋅A in Classical Mechanics goes back to Helmholtz and Clausius.
• Faraday induction nicely described historically.
• Faraday rotation with interesting stuff about the man.
• Assis, Published papers, where I find the following:
• Assis, Speed of light, with all details about different units. In WikiWorks as Assis-c.
• Assis, Speed of light, mostly about units at that time of Weber-Maxwell. Stored as Assis -units.
• Assis, Gauss and Weber and their creation of CGS units. Stored as Assis-CGS.
• Assis, Weber and Lorentz forces, history how Weber's forces unified Coulomb to Ampere force. Stored in WikiWorks as Assis-Lorentz.
• Assis, Translation of Kirchhofs paper where de derives speed of light for EM signal in wire. No displacement current at that time. But he used full continuity equation, which is equivalent. Stored in WikiWorks as Assis-Kirchhoff. Same wave equation also derived by Assis here.
• Errede, Brief History of EM
• NN, Hydrodynamic analogy for Maxwell eqs, using turbulent flow.
• G. Hall, Maxwell's electromagnetic theory and special relativity, Phil. Trans. Roy. Soc. A 366, issue 1871, 1849-1860, 28 May (2008). Summary of Maxwells ideas and papers. In WikiWorks as Maxwell-1.
• D. J. Dunstan, Derivation of special relativity from Maxwell and Newton, Phil. Trans. Roy. Soc. A 366, issue 1871, 1861-1865, 28 May (2008). Showing Maxwell eqs invariant under Lorentz in simplest case. In WikiWorks as Maxwell-2.
• Phil. Trans. Roy. Soc. A 366, issue 1871 (2008), Table of contents of memorial volume to Maxwell.
• Raymond Flood, Mark McCartney and Andrew Whitaker (eds), James Clerk Maxwell: Perspectives on his Life and Work, Excellent tale og Maxwells thinking leading to his hydrodynamical model for EM, initially inspired by idea from W. Thomson (Kelvin) as told on pp. 194 and onwards. This chapter on EM starts on p. 187 which can be read on the Amazon website.
• O. Darrigol, Electrodynamics from Ampère to Einstein, Oxford University Press (2000). Looks very good!
• M. S. Longair, Theoretical Concepts in Physics: An Alternative View of Theoretical Reasoning in Physics, with one whole chapter explaining Maxwell's mechanical clockwork ideas!

Ampere had stressed importance of electric current, but Poisson had in 1824 used picture of two magnetic fluids. Maxwell had mechanical model, electron first discovered in 1895. Poisson diskuterte også diamagnetisme.

• APS News, Ørsted's magnetic discovery, July 2008.

I 1820 viste Ørsted for første gang at magnetiske fenomen er direkte forbundet med elektrisitet. Han oppdaget at en magnetnål gjør et utslag i nærheten av en ledning som fører en elektrisk strøm. Mens nålen på oversiden av ledningen slår ut til den ene siden, slår den ut til motsatt side når den befinner seg under ledningen. Han forklarte dette ved at strømmen i ledningen skapte en «elektrisk konflikt» utenfor denne. Den gikk i sirkler rundt ledningen og påvirket de magnetiske ladningene i nålen. I ettertid omtales denne elektriske konflikten som et magnetisk felt. Dets retning er gitt ved Ørsteds lov som inneholder en anvendelse av høyrehåndsregelen.

• G.I. Verschuur, Hidden Attraction: The History and Mystery of Magnetism, Oxford University Press, Oxford (1993). ISBN 0-19-506488-7.

'Accidental discovery' in April under demonstration of heat radiation from this wire carrying current. Thought heat radiation was related to everything else caused by electricity like light. More detailed experiments in July. Wrote then four-page article in Latin. No shielding of terrestral field, had max needle deflection of 45 degree, needle not normal to wire. Effect decreased with distance, increased with thicker wire = more current. Found out that 'electric conflict' in circles around wire, not radial out or along. Both grav and electric force along connecting line, this was really new!

Ampere shielded terrestral magnetic field out by using astatic needle which can only rotate along natural field| Biot-Savart shielded with counteracting magnets. Ampere saw that needle stood normal to wire along circles.Found 1/r vaiation with distance. Changed soon to investigate magnetic interactions of currents. See article in Dropbox on Ampere and currents by Blondel. Could also show that solenoids behaved as magnets with N and S poles. Microscopic Ampere currents after suggestion by Fresnel.

See Panofsky-Phillips p.123 for simple discussion relating Ampere and Biot-Savart laws, som hos Jackson p.136 and RM p.156.

Magnus magnes ipse est globus terrestris. (The Earth itself is a great magnet.)

William Gilbert, De Magnete

• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910).
• R. Becker, Electromagnetic Fields and Interactions, Dover Book.
• A.K.T. Assis, Weber's Electrodynamics, Kluwer Academic Publishers, Dordrecht (1994). ISBN: 0-792-33137-0 in Oslo WikiWorks folder and iCloud.
• A.K.T. Assis and J.P.M.C. Chaib, Ampère's Electrodynamics, Apeiron, Montreal (2015). ISBN 978-1-987980-03-5, everything about Ampère's works and criticism of Biot-Savart contribution. Se diskusjon om Savary og Biot-Savart p.163 og på slutten.
• Reviews of Geophysics, The study of Earth's magnetism (1269–1950): A foundation by Peregrinus and subsequent development of geomagnetism and paleomagnetism, long and detailed article on whole history, also mention contribution by Hansteen. In WikiWorks
• J.D. Jackson and L.B. Okun, Historical roots of gauge invariance, Reviews of Modern Physics 73, 663-680 (2001) discusses this history of magnetic forces and potentials in great detail!!!
• RockMagnetist, Wikipedia Book on Geomagnetism, also to be found at Geomagnetism, Wikipedia Book.
• G.L. Verschuur, Hidden Attraction: The History and Mystery of Magnetism, Oxford University Press Oxford (1993). ISBN 0-19-510655-5.
• H. Erlichson, The experiments of Biot and Savart concerning the force exerted by a current on a magnetic needle, American Journal of Physics, 66 (5), 385-391 (1998).
• Kirk McDonald, Ampere and Biot-Savart, how they are related.
• CNRS, Ampère et l'histoire de l'électricité, webpages with all kinds of historical info.
• MacTutor, Savart biography
• Greek, Ampere and Biot-Savart laws
• NN, Celestial Navigation, from Bowditch’s American Practical Navigator.

Måtte innføre B og H.

• Faraday rotation with interesting stuff about the man.
• Errede, Brief History of EM

• Engelsk WP, Refrigerator magnet
• Engelsk WP, Force between magnets, Gilbert model.
• Engelsk WP, Magnetic forces, med mange definisjoner og min Minkowski-metrikk for Faraday-tensor.
• R.P. Feynman, The Feynman Lectures on Physics, Volume II, Chapter 15, Caltech, Pasadena (2003).

• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). EXCELLENT and details about Poisson's contributions to early (1824) magnetostatics on pp. 62-65. He used model with two kinds of magnetic fluids, i.e. he had not accepted Ampere's ideas. But his main contribution was concept of magnetisation, resulting in effective magnetic charges used to calculate magnetic potential Ψ as in todays theories. Also had formula for magnetic force on magnetised body in external field.
• Assis book on Ampere's Electrodynamics pp 181-182 describes also Poisson's contribution from 1824.
• Engelsk WP, Magnetic field in History section is Poisson's theoretical work mentioned.
• R.G. Brown, Duke, RGB-Duke EM lectures
• R.G. Brown, Duke, EM webpages lectures, excellent with my metric and notation. Also nice discussion of Lorentz group.
• R.G. Brown, Duke, Partial integrations of vector quantities proves that for bounded and localised current distribution
• Fitzpartick, Texas, Magnetisation and magnetic charges

${\displaystyle \int d^{3}x\,\mathbf {J} =-\int d^{3}x\,\mathbf {r} ({\boldsymbol {\nabla }}\cdot \mathbf {J} )}$

So in static case this gives ${\displaystyle \int d^{3}x\,\mathbf {J} =0}$ from ${\displaystyle {\boldsymbol {\nabla }}\cdot \mathbf {J} =0}$. In dynamic case can use eq. of continuity ${\displaystyle {\boldsymbol {\nabla }}\cdot \mathbf {J} +\partial \rho /\partial t=0}$ with harmonic time variation ${\displaystyle \partial \rho /\partial t=-i\omega \rho }$ to get ${\displaystyle \int d^{3}x\,\mathbf {J} =-i\omega \mathbf {p} }$ with total dipole moment ${\displaystyle \mathbf {p} =\int d^{3}x\,\mathbf {r} \rho }$.

• Start med Biot-Savart for stationary current distribution J and derive formula for A. Expand for large distances and isolate magnetic dipole term, following Zangwill and Oregon for integration details. Use same method to show that ∇⋅A = 0 with same methods from ∇⋅J = 0 . Just mentioned in Jackson and given as a problem in Zangwill p.334.
• Natalie, Magnetized sphere in detail
• Natalie, All EM lectures
• Errede, UIUC, Magnetic multipole expansion using Legendre polynomials. Excellent lectures
• Grensebetingelser for B- og H-felt -> B-felt trekkes inn i jern.

• Skriv magnetisk kraft ved Maxwell-tensor som utledes her. Den elektriske utledningen tas med i Maxwell-tensor.

• Magnetisk krets

Ferro, dia og para i ytre felt, trukket inn og ut.

Finnes på nynorsk WP som Einstein–de Haas-effekt. Kort og godt diskutert også av and compact told by Kirk McDonald. Den engelske WP inneholder god diskusjon med forklaring v.hj.a. g og g' - faktorer som er diskutert her:

• NN, Gyromagnetic ratios, RMP 1962.

• V. Frenkel, RMP (1979), Einstein de Haas experiment, Einstein and Stern-Gerlach. In Oslo folder.
• China, De Haas van Alphen effect, lecture notes.
• Rochester, Lectures on Solid State Physics, dHvA effect, Hall-effect etc.
• Oxford, Magnetism and band structure

• N.D. Hari Dass, The Principles of Thermodynamics, good on magnetic fields.
• M, Barrett, U. Wisconsin, Thermodynamics of magnets], very instructive. In WikiWorks as ThermodynamicsMagnets-Barrett
• Se Zangwill, pp 433-435. Litt om fri energier?
• Liu and Stierstadt, Electromagnetic forces and the Maxwell stress tensor, detailed derivation based on momentum conservation of matter and fields (AM controversy?) and nice presentation of Heaviside-Lorentz units. Force (M⋅∇)B) is here called the Kelvin force.
• Wassermann, Virginia, Thermodynamics and Magnetism, very clear discussion of thermodynamic relations. In WikiWorks as Thermal magnetism_Wassermann.
• MIT, Electromagnetic Fields and Energy, excellent lectures
• MIT, Magnetization and permanent magnets with calculation of H-field inside and outside magnetized cylinder. In WikiWorks.
• MIT, Magnetostatics. In WikiWorks.
• Engelsk WP, Rare-earth magnets

Poisson's opprinnelig utledning av sin ligning som gikk ut på at Laplace's generelle løsning ikke tilfredsstiller hans ligning inni materien, tilsvarer helt utledningen - Reitz-Milford p.188 for magnetisk felt inni magnet.

• Må også skrive om siden elektromagnetisk felt sammen med elektromagnetisme.
• Johannes Skaar, Elektromagnetisme, forelesninger for FYS1120. Lagret i WikiWorks som Johannes Skaar - EM.
• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). On pp. 420-432 is Lorentz' electrodynamics explained in detail based on ether which always is at rest and not dragged with. Lorentz force is derived from Clausius interaction term e(v⋅A - Φ) between electron charge and field as discussed on p.262. This was done in 1877 in order resolve a question which had been brought up by Helmholtz concerning the interaction between current elements. Clausius expression had also advantage that it did not depend on current consisting of two oppositely moving currents as in Weber's theory. Velocity of particle v is measured to ether which is frame where Maxwell els are valid. Lorentz assumed also no more instantaneous interaction between electrons, only through exchange of retarded potentals. For dielectrics moving could also derive Fresnel result for Fizeau experiment, and good dispersion result. Dielectrics where made up of microscopic dipoles with one electron extra and one less as in Poisson theory for magnetization. Only problem for Lorentz theory was null result of Michelson-Morley.
• F.J. Dyson, Why is Maxwell Theory so hard to understand?
• C.N. Yang, The conceptual origins of Maxwell’s equations and gauge theory, Physics Today, November 2014. Explaining Maxwell's mechanical clockworks! Skriver at W. Thomson (Kelvin) innførte magnetisk vector potential in 1851. Men var ikke det Franz Neumann i 1845? Jo, se Stackexchange med full referanse til Neumanns paper Allgemeine Gesetze Der Inducirten Elektrischen Ströme, Ann. d. Physik 143, (1) 31–44, (1846) (January 1, 1846). Se også Whittaker p.270 where he says that W. Thomson introduced A in 1846, based on elastic model for EM, independently of Neumann, Kirchhoff and Weber.
• Much more detailed history of vector potential and gauge invariance in paper by Yang and WU:
• A.C.T Wu and C.N. Yang, EVOLUTION OF THE CONCEPT OF THE VECTOR POTENTIAL IN THE DESCRIPTION OF FUNDAMENTAL INTERACTIONS, Int. J. Mod. Phys. A 21 (16), 3235–3277 (2006). In WikiWorks as Maxwell - WuYang. Also history of p - eA term in QM and coupling v⋅A in Classical Mechanics goes back to Helmholtz and Clausius.
• Heidelberg, Vorlesungen über Elektrodynamik, med bra multipolutvikling på pp 62-64 og mye mer. On p. 68 nice proof for

${\displaystyle \int d^{3}x\,\mathbf {J} (\mathbf {x} )=0}$

• Inneholder også kovariante formulering på slutten, også elektromagnetisk impulstetthet i medium. Lagret som Heidelberg EM.

• In Mehra's biography of Feynman there is a very good chapter on background and history.
• R.P. Feynman, A Relativistic Cut-off of Classical Electrodynamics, PR 1948, where he explains action-at-a-distance and ties it up with QED. Considers a situation of particle going through potential barrier as in Klein Paradox and comes to similar conclusions about positrons being electrons going backwards in time. That positrons could be described that way, Feynman writes that he was told this from Wheeler in 1941.

• Salmonsens konversationsleksikon (Projekt Runeberg), Elektronteori, EXCELLENT med mange nærliggende artikler om elektron, elektromagnetisme etc. Gir et meget godt bilde av fysikkens tilstand for over hundre år side. Alt dette betyr at jeg må skrive om og forbedre siden om elektron.
• Sommerfeld 1919, Atombau und Spektrallinien, pp 312-314 god diskusjon om Fizeau experiment, eter, etc. Også helt i begynnelsen av boken litt om fjernvirkningsteorier vs. feltvirkningsteorier.
• Nynorsk WP, Fjernverknadsteori
• SNL, Ø. Grøn, Fjernvirkningsteori
• Feynman, Nobel lecture, with action-at-distance and absorber theory.
• G. Gründler, Feynman-Wheeler absorption theory, non-relativistic and well explained.
• Feynman-Wheeler, 1949, Absorbtion theory, in Wikiworks.
• Feynman, 1950, Spacetime QED, legg merke til Appendix hvor han går over fra kvadratrot action for point particle to squared 4-velocity. In WikiWorks.
• Assis, Action at a distance, why useful using examples from Ampere, Kirchhoff, Weber etc. Stored in WikiWorks as Assis-fjernvirkning.
• Plato, Stanford, Feynman-Wheeler
• S. Schweber, QED History, chapter about Feynman', book in Oslo.
• A. Barut, Electrodynamics and Classical Theory of Fields & Particles
• L . Schulman, Time-Symmetric EM from two zeros in delta-function, in WikiWorks.
• J. Field, Feynman derivation of Lienard-Wiechert
• T. Sauer, Einstein and Feynman-Wheeler
• Deckert, München, Feynman-Wheeler PhD thesis
• AIP Oral Interview, Adrian Fokker
• A. Fokker, Ein invarianter Variationssatz für die Bewegung mehrerer elektrischer Massenteilchen, Z. Phys. 1929, first three pages...English Translation here in WikiWorks.
• H. Tetrode, Über den Wirkungszusammenhang der Welt. Eine Erweiterung der klassischen Dynamik, Zeitschrift der Physik 10, 317-328 (1922). Stored in WikiWorks.
• NN, EM without fields?, in WikiWorks
• Kiessling, Classical EM selfinteractions
• Narlikar, Absorber theory in expanding Universe
• Narlikar, Action at distance theories, with history from Gauss' comment 1845.
• Hoyle and Narlikar, Lectures On Cosmology And Action-at-a-distance Electrodynamics
• Natalie, EM lectures with Lienard-Wiechert
• Chandrasekhar, Talk about Karl Schwarzschild and beauty of GR.
• Physik Cosmos, Karl Scwarzschild bio, very good (samme som Wikipedia) with links to papers Zur Elektrodynamik III
• Karl Scwarzschild, utledning av Metrik, legg merke til enkel form på Einsteins grav. ligning.

• Bolvan, U Texas, EM lectures 2018, excellent

${\displaystyle {\Big [}q\mathbf {v} \times \mathbf {B} {\Big ]}={\mbox{C}}\cdot {\dfrac {\mbox{m}}{\mbox{s}}}\cdot {\dfrac {{\mbox{V}}\cdot {\mbox{s}}}{{\mbox{m}}^{2}}}={\dfrac {\mbox{J}}{\mbox{m}}}={\mbox{N}}}$

• Magnetisk fluks
• Magnetisk krets
• Magnetisk reluktans
• Magnetisk Induksjon
• Lorentz-kraft
• Superledere

• Trinity College, Dublin, PY5006: Magnetism and Magnetic Materials, 15 lectures on magnetism.
• Dublin, Basic magnetism, very nice.
• Dublin, Magnetism from electrons, Pauli paramagnetism and Landau diamagnetism.

• Peter Young, UCSC, Landau diamagnetism
• Peter Young, UCSC, Electrons in magnetic field
• Illinois, Magnetism, excellent about bound currents and B and H. In WikiWorks.
• Engelsk WP, Demagnetizing field

eller spolekanon.

• A. Egeland, Kristian Birkeland: The first space scientist, Journal of Atmospheric and Solar-Terrestrial Physics 71 (2009) 1749–1755. In WikiWorks.
• A. Egeland, Birkeland's electromagnetic gun: a historical review, IEEE Transactions on Plasma Science, 17 (2), April (1989).
• A. Egeland, Mannen bak Norges viktigste oppfinnelse, intervju i forskning.no 2017.
• Egeland and Burke, Carl Størmer: Auroral Pioneer
• US Patent
• Lucy Jago, The Northern Lights: The True Story of the Man Who Unlocked the Secrets of the Aurora Borealis
• UiT, Aurora Borealis
• NN, Auroral Oval, lang tekst
• Plasma Universe, Kristian Birkeland
• K. Rypdal and T. Brundtland, Birkeland's Terrella Experiments
• UiO rektor O.P. Ottersen, Bill Gates og Birkelands kanon
• NN, Coil guns
• Nick Eyre, Magnetic calculations behind coil gun, with experiments. Excellent and in WikiWorks.
• Gutenberg Project, Kristian Birkeland bio, good on Birkeland currents.
• Egeland book?, Birkeland works and publications
• Aftenposten 2006, [Interview med Egeland som pensjonerte seg 64 år gammel], men arbeider fortsatt.
• A. Egeland, Samarbeid mellom Birkeand og Sam Eyde, pp290-321, Agder Vitenskapsalademi (2012).
• Deshpande, Ultracapacitors, modern coil guns and DARPA.
• NN video, Homemade Gauss gun with magnets and steel balls
• Coilgun Systems, Good magnetic theory around coil guns, for beginners.

Panofsky-Phillips pp 140-143 shows that B- and H-fields for permanent magnets can be calculated from scalar potential Ψ with

${\displaystyle \mathbf {H} =-{\boldsymbol {\nabla }}\Psi }$

and B from curl of vector potential A as usual. Then Ψ is given by surface magnetic charges, while A is given by surface currents. Outside material PP shows that these two fields then agree. Also very clear in Jackson's book. Må skrives a la Panowsky-Phillips og Zangweil med bruk av effektive magnetiske ladninger og strømmer, bl a for å beregne magnetiske krefter som viser seg å være gitt ved Maxwells tensor som vist i Zangweil.

In book by Longair Theoretical Concepts p. 80 it is stated that it was Poisson who introduced scalar potential Ψ for magnetic field.

Jackson Classical Electrodynamics gives good explanation of B and H-fields by microscopic averaging. And calculates clearly resulting, internal B- and H-fields of ferromagnetic sphere exposed to external B-field giving saturation and then turned off.

• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). EXCELLENT and details about Poisson's contributions to early (1824) magnetostatics on pp. 62-65. He used model with two kinds of magnetic fluids, i.e. he had not accepted Ampere's ideas. But his main contribution was concept of magnetisation, resulting in effective magnetic charges used to calculate magnetic potential Ψ as in todays theories. Also had formula for magnetic force on magnetised body in external field.

• Webpages, Everything about magnets, starting with Gilbert, Halley etc
• Gilbert, De Magnete in engelsk Wikipedia.
• RockScientist, Why science in Wikipedia
• RockScientist, Engelsk WP, History of geomagnetism, best available, full history
• Heilbron, Magnetic History, good and detailed.
• Southampton,Some history
• Engelsk WP, Timeline of electromagnetism and classical optics, good on Ampere's contribution.
• J.J. Roche, B and H, the intensity vectors of magnetism: A new approach to resolving a century-old controversy, American Journal of Physics, 68 (5), 438 - 449 (2000).
• New World Encyclopedia, Short magnetic history. Tells that Coulomb measures inverse-law for forces between magnetic poles. See also Zangwill p.436 how this comes out in modern theory.
• Oregon, Magnetostatics, with multipole expansion and good notation. In Oslo folder Oregon EM.
• UW, Technical applications of magnets, interesting
• Deutsch, Magnete und ihre Wirkung
• Stern-Gerlach-eksperiment er omtalt hos Øverbø, Chap-12.

SI-enheten for feltstyrke er tesla, og enheten for magnetisk fluks er weber. En tesla er en svært stor enhet, jordens magnetfelt er på ca. 30 – 60 μT.

• Kirk McDonald, Lecture7 - Steady currents and magnetism explaining Ampere, Biot-Savart, Gauss and Hall-effekt.
• Kirk McDonald, Lecture8 - Magnetization and magnetostatics, magnetic circuits.
• Kirk McDonald, Magnetic forces, also on extended, magnetic objects.
• Kirk McDonald, Magnetic energy and work
• Kirk McDonald, Magnetic forces in linear media and calculational details
• Kirk McDonald, Magnetic forces and Maxwell tensor
• Kirk McDonald, Electron motion in magnetic monopole/dipole fields, from Birkeland, Størmer, Poincare to Dirac and Schwinger.

En atomkjerne, f.eks. et proton, roterer og har derfor angulært moment (spinn). Vanligvis roterer disse tilfeldig, dermed opphever hverandres felt. Når vi har en magnet roterer et større antall atomer i samme retning og skaper et felt. Nord og sør på en magnet roterer i motsatt  retning. 

• God fremstilling på fransk WP, med superledende bilde og enkel utledning av magnetisk stress.

Ferromagnetisme finnes allerede i stub utgave.

• Italiensk WP, Ferromagnetismo med Heisenberg model and mean-field solution.
• Engelsk WP, Spontaneous magnetization, can easily be expanded

Utvid elektron. Ble kallt elektrisk atom av Helmholtz i 1881 in his famous Faraday Lecture held on 5 April 1881 at the Chemical Society in London , electron by Stoney i 1891.

• Engelsk WP, Electromagnetic mass, Lorentz and electron mass, 4/3 factor etc.
• Engelsk WP, Abraham-Lorentz force, pre-acceleration etc.
• O. Darrigol, The Voltaic Origins of Helmholtz’s Physics of Ions, history of how electron concept arose.
• D. Cahan, Hermann Von Helmholtz and the Foundations of Nineteenth-Century Science, starts out with vis viva, energy conservation, Weber electrodynamics and much more.
• Siegmund Brandt, The Harvest of a Century: Discoveries of Modern Physics in 100 Episodes, many interesting, short stories.

Finnes allerede som magnetisk monopol. Utvid med [Errede forelesning som finnes i Oslo folder Errede EM. Ta også med vektorpotensial for Dirac-streng beregnet hos Zangwill p.344.

• MIT, Poynting vector and Maxwell stresses, very clear! In WikiWorks where much more EM in this lecture series.
• MIT, Electric and magnetic forces. Direct derivation of Maxwell stress tensor with examples. Contains example of cylindrical current-carrying conductor in external field. Includes self-interactions of field created by current, but these give no net forces. Compare this with discussion by Kirk McDonald. In Oslo folder Electrostatics.
• NN, Magnetic stress tensor with magnetization
• Illinois, Maxwell stress tensor with many examples. In Oslo folder Electrostatics.
• Zürich, Maxwell stress tensor and radiation pressure. In Oslo folder Electrostatics.
• Kirk McDonald, Maxwell stress tensor and radiation pressure. different ways. In Oslo folder Kirk McDonald.
• Stackexchange, Maxwell stresses for beginners, sign illustrated.
• NN, Simple derivation for magnetic field
• Liu and Stierstadt, Electromagnetic forces and the Maxwell stress tensor, detailed derivation based on momentum conservation of matter and fields (AM controversy?) and nice presentation of Heaviside-Lorentz units. Force (M⋅∇)B) is here called the Kelvin force.

• Singapore, Basics for driven HO. In WikiWorks.
• Ohio, Green's function for driven HO as particular integral. In WikiWorks.
• Karoly Simonyi, A Cultural History of Physics, BEAUTIFUL, contains lots of stuff I want to read.

• NN, NTNU eksamensoppgave hvor ordet multipolutvikling brukes.

• Natalie, Kramers-Kronig relations and Drude model
• Natalie, Dipole radiation, very general and nice!
• Natalie, Antenna radiation, more general
• Natalie, All EM lectures
• Blog, Multipole expansion
• UCSD, Magnetic moment related to angular moment.

• Suzanne Fielding, University of Durham, Lectures on fluid mechanics.

• Stackexchange, Energy-momentum-tensor for dust
• Winnipeg, Energy-momentum-tensor
• Warwick, Number conservation and energy-momentum, good!
• MIT, Stress tensor in hydrodynamics
• NN, Fluid mechanics, relevant presentation
• Warnemünde, Hydrodynamics
• J.W. van Holten, Relativistic fluid mechanics, covariant and very good!
• Frankfurt, Relativistic hydrodynamics, with applications to quark-gluon plasma.

• Engelsk WP, Continuity equation
• Durham, Cont equation for hydrodynamics, also momentum conservation.

God innledning i Griffiths EM bok. Legge merke til at på nn WP er Laplace-ligning det samme som Young-Laplace-ligning. Dette bør jeg kalle Young-Laplace-ligning som på engelsk WP og benytte notat fra Stavanger.

Så etter dette må skrive om Poissons ligning.

• Engelsk Wp, About Legendre and spherical harmonics
• Laplace, Mécanique Céleste, 3rd book, early works on ellipsoidal bodies in Newtonian gravity.
• U Colorado, Laplace equation and mean value theorems
• Poisson , Mémoire sur la Distribution de l'Électricité à la Surface des Corps Conducteurs, Mém. de l'Institut, 12 (pt. 1), 1–92. Publisert i 1812. Omtalt i M. Longairs bok Maxwell's enduring Legacy about the Cavendish lab )in Berlin), as very famous on p.10. Here he also published his Poisson eq. In 1826 he published same equation for magnetic, scalar potential.
• Engelsk WP, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism by George Green. Here it is stated that Poisson solved charge distribution on ellipsoid.
• NN, Laplace equation history background
• W. W. Rouse Ball, A Short Account of the History of Mathematics
• W. W. Rouse Ball, in A Short Account of the History of Mathematics, Laplace biography.
• W. W. Rouse Ball, in A Short Account of the History of Mathematics, Poison biography
• R. Becker, Electromagnetic Fields and Interactions, Dover Publications, New York (1982). ISBN 0-486-64290-9, used by Kirk McDonald.
• R. Becker, Electromagnetic Fields and Interactions, Dover Publications, New York (1982). ISBN 0-486-64290-9, used by Kirk McDonald. On p.226 shown how radiation pressure can be obtained direkte from Maxwell tensor.
• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910).
• F. Dyson, George Green history and comments
• D. M. Cannell and N. J. Lord, George Green, Mathematician and Physicist 1793-1841, The Mathematical Gazette 77 (478), 26-51 (1993).
• Elizabeth Garber, The Language of Physics: The Calculus and the Development of Theoretical ..., details about works by Laplace, Poisson, Ampere, Fourier, ...
• Elizabeth Garber, S. Posson and his contributions
• ed. I. Grattan-Guinness Companion Encyclopedia of the History and Philosophy of the ..., Volum 2, details about Poissons electrostatics plus more about Ampere, Gauss, Weber. Important
• Isaac Todhunter, A History of the Mathematical Theories of Attraction and the Figure of the Earth, much about MacLaurins calculation of attractions of ellipsoids.
• NN, On Maclaurin and attraction of ellipsoids
• Niccol- Guicciardini, The Development of Newtonian Calculus in Britain, 1700-1800, Maclaurin and Clairaut and Simpson, shape of Earth.
• Subrahmanyan Chandrasekhar, Newton's Principia for the Common Reader
• John L. Greenberg, The Problem of the Earth's Shape from Newton to Clairaut
• G. Iurato, History of Maclaurin ellipsoids, arxiv-1409.3858.
• Karp, Newton's theorem inside hollow ellipsoid
• NN, Calculating potential from ellipsoid
• MacTutor, Poisson biography som er brukt i norsk WP om Siméon Denis Poisson
• Curtright et al, Charged Ellipsoids
• Curtright et al, Electric field from charged line segment, also on arXiv
• Physicstasks, Electric field from charged line segment
• Youtube, Electric field from charged line segment
• Kirk McDonald, Conducting Spheroids
• Kirk McDonald, Lecture 3 - Electric energies and Maxwell stress tensor.
• Kirk McDonald, History of electrical conductors, magnets and much more
• MIT, Electric fields and potentials
• MIT, Maxwell stress tensor
• MIT, Magnetic force and levitation
• Griffiths, Conducting needle
• NN, Griffiths book solutions
• J.A. Stratton, Electromagnetic Theory
• Andrew Zangwill, Modern Electrodynamics, with charged line segment and ellipsoidal equipotentials exactly done.
• Edward M. Purcell and David J. Morin, Electricity and Magnetism, Cambridge University Press, Cambridge (2013). ISBN 978-1-107-01402-2. Excellent.
• Illinois, Magnetism, excellent about bound currents and B and H. In WikiWorks.
• Illinois, Maxwell stress tensor, excellent detailed notes
• Illinois, Poynting paradox, in Oslo WikiWorks folder.
• Illinois, Maxwell paradox, in Oslo WikiWorks folder.

• Struik, History of Mathematics says that Poisson found his equation in 1812 assuming constant density. General proof first by Gauss in 1839. Gauss had already in 1813 shown that volume integrals can be transformed into surface integrals.
• R.D. Richtmyer, Principles of advanced mathematical physics, Springer-Verlag, New York (1978). ISBN 0-387-08873-3.

• Karoly Simonyi, A Cultural History of Physics, BEAUTIFUL, contains lots of stuff I want to read.
• Mathpages, Poisson eq for gravity and cosmological constant.
• Taiwan, Simple derivation of Posson eq, essentially using Gauss theorem
• MIT, Poisson equation from Laplace eq.
• DAMTP, Poisson eq in gravity
• UiB, Poisson eq background
• Encyclopedia Math, Poisson equation original reference publication 1813
• C. O’Raifeartaigh et al, One Hundred Years of the Cosmological Constant:, discusses original sign of cosmological constant etc.

• H. Lamb, Hydrodynamics, Dover Publications, New York (1991). ISBN 978-0-486-60256-1.
• G. Falkovich, Fluid Mechanics: A Short Course for Physicists, Cambridge University Press, New York (2011). ISBN 978-1-107-00575-4. Good on Eulerian-Lagrangian description.
• Malham, Introductory Fluid Mechanics, excellent with derivation of moving control volumes. Stored in WikiWorks.
• Heidelberg, Hydrodynamic stress tensor
• München, Introductory fluid dynamics, very nice! Stored in WikiWorks.

• J. Bain, History of Light, excellent lectures stored in History of Light

• Young and Wave Theory
• Malus and Polarization
• Arago and Biot
• Fresnel Wave Diffraction
• Huygen's Principle
• The Wave Theory
• Fresnel's Unification
• Ampere and Faraday
• Fields and Lines of Force
• Maxwell, contains excellent description of Maxwell's mechanical model.
• FitzGerald and Lodge
• Heaviside and Aether Models, also his telegraph equation
• Maxwell and EM Waves, also about telegraph equation
• Maxwellian Heyday, about Hertz experiment
• Advent of Electron
• Electromagnetism and SR, derives Fresnel drag coefficient.
• EM and QM, heat radiation and BS quantization
• The Light Quantum

• Brush, Light-quantum Hypothesis
• Darrigol, Quantized Matter Waves
• Darrigol, Electrodynamics
• Darrigol, Genesis of Special Relativity
• Kragh, Relativistic Quantum Mechanics, stored in Elektrodynamikk
• Schweber, Particle Physics
• Suman, Seth QM and EM
• MathPages, Ole Rømer and the speed of light, kanskje kan benyttes i utvidelse?
• K.S. Mendelson, The story of c, Am. J. Phys. 74 (11), 995-997 (2006). Paper coli in folder FYS1120 lecture notes, UiO.

Rett opp og utvid elektron med ref til Lorentz og Zeeman-effekt.

• R. Ferraro, From æther theory to special relativity, very basic.
• NN, Lorentz bio from Holland with history of electron discovery.
• Eter (fysikk) bør utvides. Tysk versjon er meget detaljert. Se Britannica 9th ed. 1878, Ether, written by Maxwell. Also of much interest Aether drag hypothesis
• J. Larmor, Aether and Matter, Cambridge University Press (1900), med mye interessant historie i begynnelsen.
• Wikibooks, Spesial Relativity and Aether, ether in the US.
• Citizendium, History of ethers, quite detailed about Descartes, Hooke, Huygens and so on...
• NN, Electrodynamics and Special Relativity, very good, based on Darrigol book. Derives Fresnel drag factor.
• Sean Carroll, Ripples in the aether
• J. Stachel, Einstein and ether-drift experiements, Physics Today, May 1987.
• Kostro, Einstein's new ether after GR.
• Blog, Abraham-Minkowsky controversy, with new experimental test.
• Skullinthestars blog, Arago and Fresnel optical experiments
• NN, More detailed discussion of abberation, Arago and Fresnel experiments
• Mathpages, Explaining Fizeau
• NN, Explaining Fizeau, from Fresnel to Lorentz/Einstein.
• Russell McCormmach, Historical Studies in the Physical Sciences.
• Sommerfeld 1919, Atombau und Spektrallinien, pp 312-314 god diskusjon om Fizeau experiment, eter, etc. Også helt i begynnelsen av boken litt om fjernvirkningsteorier vs. feltvirkningsteorier.
• H. Kragh, Higher Speculations, with chapter on electron, Lorentz and electron theories.
• Einstein (1895), Einstein's First Paper on Ether in Magnetic Fields. In WikiWorks.
• Einstein (1920), Ether and the Theory of Relativity, lecture in Leyden.
• Engelsk WP, Luminiferous aether, very good overview with links.
• Engelsk WP, Lorentz ether theory
• Engelsk WP, Aether theories, very good, read also Discussions.
• Engelsk WP, Aether drag theories
• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). On pp. 420-432 is Lorentz' electrodynamics explained in detail based on ether which always is at rest and not dragged with. Lorentz force is derived from Clausius interaction term e(v⋅A - Φ) between electron charge and field as discussed on p.262. This was done in 1877 in order resolve a question which had been brought up by Helmholtz concerning the interaction between current elements. Clausius expression had also advantage that it did not depend on current consisting of two oppositely moving currents as in Weber's theory. Velocity of particle v is measured to ether which is frame where Maxwell els are valid. Lorentz assumed also no more instantaneous interaction between electrons, only through exchange of retarded potentals. For dielectrics moving could also derive Fresnel result for Fizeau experiment, and good dispersion result. Dielectrics where made up of microscopic dipoles with one electron extra and one less as in Poisson theory for magnetization. Only problem for Lorentz theory was null result of Michelson-Morley.
• G. Holton and S.G. Brush, Physics, the Human Adventure, Rutgers University Press, New Brunswick, New Jersey (2001). ISBN 0-8135-2908-5. pp 370-380 brukbart om Maxwells mekaniske teori for EM og enhetlig eter for varmetransport og stråling.
• Engelsk WP, Lorentz ether theory, gives very good overview, including contributions of Poincare and Einstein!
• Joseph Larmor, Aether and Matter, very good intro to state of thinking 1900.
• Tam Hunt, Santa Barbara, Ether and particle physics, with quotes from Einstein, Wilzcek, Krauss etc about new ether from Higgs field etc. Stored in WikiWorks as Higgs Field as New Ether.

1. # # # # # #

• Johannes Skaar, NTNU, Forelesninger TFE4120: Elektromagnetisme, Youtube (2017).
• Walter Levin, MIT, Lectures on Electricity and Magnetism, Youtube (2015).

• NN, Princess Caroline and Leibniz

• D. Halliday and R. Resnick, Fundamentals of Physics, John Wiley & Sons, New York (1988). ISBN 0-471-63736-X. Uses units and notation that I can follow, i.e. V for potential and U for potential energy.

Kunne bruke noen enkle, matematiske beregninger til beregning av feltlinjer fra gitt feltvektor. ∇²φ = 0.Enkelt eksempel fra UCLA eller her.

• Italiensk WP, Linea di campo
• UiB, Stream lines Good!
• Bielefeld, Hydrodynamics and 2-dim complex potentials with dipole field.
• MIT, Flows and potentials
• Oxford, Lecture on hydrodynamic flow
• Texas, 2-dim flows

Generelt om elektriske og magnetiske dipoler på engelsk WP. På tysk og italiensk er det egen side om magnetiske dipoler. Men på engelsk WP er det stor artikkel om magnetic moment, også på magnetisk moment. Også på nn om magnetisk dipol. På slutten ta med litt om multipolutvikling.

• F. Ravndal, UiO, Maxwells ligninger FYS1120, notat (2009).
• Johannes Skaar, Maxwells ligninger, Youtube. Aether, Michelson-Morley, Lorenz-betingelse. Bølgeligning med kilde.
• Johannes Skaar, 4: Coulombs lov, skalart potensial, elektroskop.
• Johannes Skaar, 13: Entydighet av løsning av Poisson ligning. Ideell leder definert av at inneholder frie ladninger? Eksperiment med Al bouncing ball mellom to Al plater.
• Johannes Skaar, Prinsipp for lynavleder, Faraday bur.
• Engelsk WP, Signal strengths in telecommunication
• Lover og matematikk
• Beregn felt fra sfærisk fordeling med Newtons skallteorem som er sfærisk versjon av mer generell Gauss' lov. Se spansk WP Ley de Gauss.
• Italian, Electrical fields and surface charges on current transmission lines. In Wiki folder. With ref. to Jackson.
• NN, Charge density on ellipsoid calculated...
• Griffiths, Charges needle with ref. til Smythe book.
• Griffiths, Introduction to Electrodynamics, with ellipsoid problem on p.111.
• Kirk MacDonald, Electrostatic problems with spheres and ellipsoids.
• Kirk MacDonald, Surface charge on ellipsoid - SOLVED geometrically!!
• New Zeeland, Electrostatics of toroids and surface charges.
• Max field 10^9 V/m in book by Grant and Phillips Electromagnetism. Atmosfærisk elektrisitet gir feltstyrke opp til 100 V/m nær jorden ifølge engelsk versjon. Mye bedre i dansk versjon og nederlandsk. Felt fra friksjon ved å gå på teppe up to 500 kV/m. Computer screen at distance 30 cm 10-20 kV/m. Nyttig å konsultere Elektrisk gjennomslag.
• Schwinger limit, Schwinger limit
• FNAL, Elementary particle accelerators. First Cockroft-Walton in 1931 high voltage 10^6V = 1 MV.
• NN, Cyclotron with numerical example
• Brittanica, Workings of accelerators nicely explained.

• 
  Det integrerade flödet är proportionellt mot de inneslutna källornas styrka.
• 
  Utan källor eller sänkor är det integrerade flödet noll.
• 
  Flödets ytintegral för en dipol är noll.

Benytt disse figurene i oppdatering av Gauss' lov. Utvid eksisterende Elektrostatikk. På engelsk WP også mye brukbart om Statisk elektrisitet på slutten av artikkelen. Bevis Gauss teorem her på samme måte som i Reitz-Milford. Konsulter elektroskop og elektrisk leder med felt alltid normalt. En del praktiske eksempel bruk av Gauss på fransk WP.

Godt forklart på engelsk WP, tysk og italiensk. Russisk versjon gir ekspansjon vha Legendre-polynom for sylindersymmetri. See also Spherical multipole expansion og spesielt Axial multipole moments med god figur!

• U Michigan, Legendre expansion.

• Lover og matematikk
• Beregn felt fra uendelig plan fordeling med integrasjon og Gauss' lov
• Ledere og isolatorer
• Faradays bur
• Elektrisk potensial
• Elektromagnetisk induksjon
• Energitetthet
• Hawaii, Faraday Ice Pail experiment.

Se italiensk versjon og mange andre. Svensk versjon inneholder mange gode figurer. Beregning av elektrisk felt fra Gauss' lov godt gjort på tysk versjon med praktiske anvendelser. Hva er historien om Gauss' lov hvis Gauss-Weber var negativ til elektrisk felt begrep?

Field history from Assis book on Gauss-Weber electrodynamics in ICloud: Lagrange introduced scalar potential in gravity in 1777. In 1782 Laplace found his equation for this field, published in 1785. In 1811 Poisson introduced scalar potential in electrostatics and 1813 found his equation for this inside matter. In Appendix A of this book also history of magnetic force law F = qv×B, very complicated!! Correct form was first stated by Heaviside in 1889 - after Maxwell dead. Magnetic vector potential A was proposed by Franz Neumann in 1845.

In same book p.74 stated that it was Helmholtz who sorted out conservation of energy, and in 1847 introduced kinetic energy 1/2mv^2 instead of vis viva mv^2. Also detailed description of Ampere's law for magnetic forces. But his original force law was soon forgotten. Instead in 1845 came Grassmann's formulation which is the one we use today. Grassmann found this modern formulation as an exercize in using his antisymmetric vector product!

• CNRS, Discussion of Ampere vs Grassmann magnetic force laws
• J.D. Jackson and L.B. Okun, Historical roots of gauge invariance, Reviews of Modern Physics 73, 663-680 (2001) discusses this history of magnetic forces and potentials in great detail!!!
• HyperPhysics, Solving Laplace-Poisson eqs inside spherical charge distribution.

From other source: Historisk idea of field important contribution from Laplace who 1785 showed that to calculate gravity from several masses more practical to introduce scalar potential \Phi. Then force given by gradient. This field outside masses satisfied Laplace equation, i.e. the first field equation. This field was found by adding the field from each mass, decreasing as 1/r with distance. Then 1813 Poisson showed that inside masses field satisfies Poisson equation. He also proposed that this could be used for electrical problems. He also showed that potential on conductor surface must be constant.

• Mathpages, First speed of light, in sec.8.6 says that speed of light first obtained by Kirchhoff in 1848 from ratio of electromagnetic to electrostatic units. Then again in 1858 by B. Riemann who presented a theory based on the hypothesis that electromagnetic effects propagate at a fixed speed, and then deduced that this speed must equal the ratio of electromagnetic and electrostatic units, i.e., 1/c = \sqrt(\epsilon_0 \mu_0). This is web version of book by Kevin Brown : Reflections on Relativity which is very rich on interesting comments. For an explanation of how speed of light appears from such considerations, consult footnote on p.227 of Whittaker book. Here in connection with Wener and his problem in Hannover caused by Queen Victoria, also explained p.225 Fechner's proposal that current consists of two oppositely-moving streams of charges of opposite signs. On p.231 describes B. Riemann's theory from 1861 for the force between two moving charges. On pp.257-258 described how Kirchhoff derived telegraph equation and finding speed of light. On p.261-262 told what Helmholtz did to reconcile Weber theory with Ampere-Neumann.

• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). EXCELLENT

At the end of this section 8.3 there is discussion of Gauss' law for two moving charges. In 1835 (discovered after his death) wrote force law, but had problem. Changed slightly by his friend W. Weber in 1845 removing one term getting his own force law. It was used by Weber as the basis of his theory of electrodynamics published in 1846. Indeed this formula served as the basis for most theoretical studies of electromagnetism until it was finally superseded by Maxwell's theory beginning in the 1870s.

• The name electrodynamics was given first time by Ampere in his Memoire from 1825 describing magnetic interactions between currents, i.e. charges in motion. (Whittaker p.89)
• W. Lewin, MIT, Electrostatic shielding
• Student of Kirk MacDonald, Was Feynman wrong about shielding?
• Trefethen, related to above, Why Feynman was wrong?
• Trefethen, Oxford, Mathematics of Faraday Cages
• Oxford, More mathematics of Faraday Cage
• LSU, Shielding and Faraday nicely explained.
• Colorado, Gauss' law for pedestrians
• UMass, Elementary about Faraday Cage with nice illustrations.
• J.M Thomas, Michael Faraday and The Royal Institution: The Genius of Man and Place, Taylor & Francis Group, New York (1991). ISBN 0-7503-0145-7.

Bis zum Nachweis elektromagnetischer Wellen durch Heinrich Hertz bestand die Frage, ob die zwischen elektrischen Ladungen wirkenden Kräfte unmittelbar im Sinne einer Fernwirkung oder unter Vermittlung durch den Raum (Nahwirkung) zustandekommen.

• Typisch für eine Fernwirkungstheorie ist das coulombsche Gesetz: Die wesentlichen Elemente der Anordnung, die Ladungen, treten (neben den erforderlichen Angaben zur Geometrie) sowohl in den Gleichungen für die Kraft als auch in den Gleichungen für die Energie auf. Ladungen an zwei verschiedenen Orten wirken aus der Ferne aufeinander; von einer Vermittlung durch den Raum ist keine Rede. Das elektrische Feld ist in der Fernwirkungstheorie nur eine nachgeordnete Rechengröße.

• In einer Nahwirkungstheorie bestehen hingegen nur zwischen solchen Größen Zusammenhänge, die am gleichen Ort gleichzeitig vorhanden sind. Ein Beispiel für eine Nahwirkungstheorie sind die Maxwellschen Gleichungen. Nach diesen Vorstellungen kommt die größte Bedeutung bei den elektrischen Erscheinungen den Feldern zu. Die elektrische Energie wird nicht als den Ladungen und Leitern anhaftend betrachtet, sondern befindet sich in den Isolatoren und im Vakuum und kann durch diese hindurch transportiert werden.

Solange nur langsame Veränderungen der elektrischen und magnetischen Größen betrachtet werden, ist es nicht entscheidend, ob man mit den physikalischen Erscheinungen die eine oder die andere Vorstellung verknüpft. Berücksichtigt man jedoch, dass sich mit elektromagnetischen Wellen Impuls und Energie im Raum ausbreiten können, so lässt sich die Vorstellung einer Fernwirkung nur schwer mit den Beobachtungen in Übereinstimmung bringen.

Zusammenfassend geht man aus heutiger Sicht davon aus, dass die Wechselwirkung zwischen den Ladungen erst vom elektrischen Feld vermittelt wird. Da die Kraft vom elektrischen Feld an der betreffenden Stelle abhängt, aber nicht direkt vom elektrischen Feld an anderen Punkten, handelt es sich um eine Nahwirkung. Ändert sich die Position einer der Ladungen, so breitet sich die Änderung des Feldes mit Lichtgeschwindigkeit im Raum aus. Eine relativistische Betrachtung des elektrischen Feldes führt zum elektromagnetischen Feld. Dieses kann Impuls und Energie aufnehmen und transportieren und ist daher als ebenso real anzusehen wie ein Teilchen.

A little about connection to QHE can be found on German WP which is very good. Check also Kibble Balance which is also called Watt Balance.

• M Eckert, Arnold Sommerfeld: Science, Life and Turbulent Times 1868-1951,
• J.D. Barrow, The Constants of Nature - From Alpha to Omega, Pantheon Books (2002). ISBN 978-0-22-406135-3.
• J.D. Barrow, Time-varying constants
• N.J. Carron, arxiv-1506.01951, Babel of Units, very good history of electromagnetic units. In Dropbox.
• von Klitzing, Explanation of relation between Klitzing constant and fine structure constant. On Berliner Schreibtisch.
• Physics Teacher, History of cgs, Giorgio, MKS and SI units
• Harvard, Short summary
• NIST, Results from QHE
• NIST, Background to Watt Balance and determination of Planck's constant.
• James B. Westgard, Electrodynamics: A Concise Introduction, with nice survey of relation between different units.
• English WP, 2018 proposed redefinition of SI base units, says it all!!!
• NN, QHE and von Klitzing constant. On Berliner Schreibtisch.
• Backreaction, QHE nicely presented!
• CERN, HEP natural units
• Hsu, Natural units and Planck ideas. Arxiv-1112.6332. Reducing the number of physical units down to one? Not natural to measure NS-distance in meters and EW-distance in miles. Then distance D = \sqrt{x^2 + k^2y^2} where conversion factor k = 1609 m/mile. From Wheeler-Taylor book.
• Klaus von Klitzing, Metrology in 2019, Nature Physics 13, 198 (2017). About natural units based on fixed values for fundamental constants, realizing Planck's vision.
• NIST, New natural SI units
• Sciencealert, New natural SI units
• NN, Natural units simply explained, Nature Physics 12, 1082 (2016).
• NN, SI 2018 natural units , [Nature Physics 12, 4–7 (2016)
• J, Preskill, Caltech, All lectures
• P. Ramond, Lectures on Electroweak theory, TASI 2011.
• CERN, Fine-structure constant at M_Z
• Donoghue, Golowich and Barry Holstein, Dynamics of the Standard Model, Cambridge University Press, New York. (1996). ISBN 0-521-47652-6.
• Jegerlehner, Vacuum polarization and electro-weak theoy, running couplings and dispersion relations (2009). In Dropbox.
• Wolfram MathWorld, Wyler's Constant, about exact values for α.
• H. Kragh, Magic Number: A Partial History of Fine-Structure Constant, Arch. Hist. Exact Sci. 57, 395-431, 2003. On Berliner Schreibtisch. Here is also explained how Sommerfeld calculated the splitting of the H_α doublet in H (and He) from his realistic formula and Pachen confirmed it experimentally. When Schrødinger later did his equation, he used firt KG equation but found this splitting to be wrong by a factor of 8/3. Thus he rejected it.
• Caltech, Hydrogen spectrum, H_α splitting already seen by Michelson 1892.
• NN, Erwin Schrödinger, where these splittings are discussed.
• Backreaction, Splitting of H_α from measurements give Δν = 10 GHz, corresponding to Δλ = 0.015 nm.
• Cambridge, Atomic physics and fine structure
• Oxford, Atomic physics, very clear. Also derives LS-splitting in rest frame of nucleus due to electric field induced by moving electron. Thus avoids Thomas correction. Stored in iCloud as Oxford atomic physics.
• Dutch lecture, Atomic spectra with Bahcall result of constancy of fine structure constant.
• NN, Spin-orbit-couplings with all transitions making up H_α line in Hydrogen shown end of paper. This page is stored as H_alpha splitting in Dropbox.

• Ta med metode med speilbilder, og anvend på ladning utenfor metallisk plan.

Se italiensk versjon og mange andre. Svensk versjon inneholder mange gode figurer. Beregning av elektrisk felt fra Gauss' lov godt gjort på tysk versjon med praktiske anvendelser. Hva er historien om Gauss' lov hvis Gauss-Weber var negativ til elektrisk felt begrep?

Field history from Assis book on Gauss-Weber electrodynamics in ICloud: Lagrange introduced scalar potential in gravity in 1777. In 1782 Laplace found his equation for this field, published in 1785. In 1811 Poisson introduced scalar potential in electrostatics and 1813 found his equation for this inside matter. In Appendix A of this book also history of magnetic force law F = qv×B, very complicated!! Correct form was first stated by Heaviside in 1889 - after Maxwell dead. Magnetic vector potential A was proposed by Franz Neumann in 1845.

In same book p.74 stated that it was Helmholtz who sorted out conservation of energy, and in 1847 introduced kinetic energy 1/2mv^2 instead of vis viva mv^2. Also detailed description of Ampere's law for magnetic forces. But his original force law was soon forgotten. Instead in 1845 came Grassmann's formulation which is the one we use today. Grassmann found this modern formulation as an exercize in using his antisymmetric vector product!

• CNRS, Discussion of Ampere vs Grassmann magnetic force laws
• J.D. Jackson and L.B. Okun, Historical roots of gauge invariance, Reviews of Modern Physics 73, 663-680 (2001) discusses this history of magnetic forces and potentials in great detail!!!
• AIP, Basic Electrostatics with capacitance of spheres/cylinders. Stored in 2023.

From other source: Historisk idea of field important contribution from Laplace who 1785 showed that to calculate gravity from several masses more practical to introduce scalar potential \Phi. Then force given by gradient. This field outside masses satisfied Laplace equation, i.e. the first field equation. This field was found by adding the field from each mass, decreasing as 1/r with distance. Then 1813 Poisson showed that inside masses field satisfies Poisson equation. He also proposed that this could be used for electrical problems. He also showed that potential on conductor surface must be constant.

• Mathpages, First speed of light, in sec.8.6 says that speed of light first obtained by Kirchhoff in 1848 from ratio of electromagnetic to electrostatic units. Also here tells about Gauss and his force law between moving charges. This was the basis for Weber's later force law. Then again in 1858 by B. Riemann who presented a theory based on the hypothesis that electromagnetic effects propagate at a fixed speed, and then deduced that this speed must equal the ratio of electromagnetic and electrostatic units, i.e., 1/c = \sqrt(\epsilon_0 \mu_0). This is web version of book by Kevin Brown : Reflections on Relativity which is very rich on interesting comments. For an explanation of how speed of light appears from such considerations, consult footnote on p.227 of Whittaker book. Here in connection with Weber and his problem in Hannover caused by Queen Victoria, also explained p.225 Fechner's proposal that current consists of two oppositely-moving streams of charges of opposite signs. On p.231 describes B. Riemann's theory from 1861 for the force between two moving charges. On pp.257-258 described how Kirchhoff derived telegraph equation and finding speed of light. On p.261-262 told what Helmholtz did to reconcile Weber theory with Ampere-Neumann.

• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). EXCELLENT

Gauss' law = Gauss' flux theorem was formulated in 1835, but was not published before 1867. See tysk WP about Gauss' integralsatz.

• C.H. Stolze, A History of the Divergence Theorem, Historia Mathematica 5 (4), 437-442 (1978). On Schreibtisch.
• English WP, Weber electrodynamics, what is this?
• Stackexchange, Some discussion of Weber electrodynamics
• NN, Everything about Ampere, Gauss and Weber and magnetic interactions. Quacks?
• A.K.T. Assis, Weber's Electrodynamics, Springer Science, Dortrecht (1994). ISBN 978-90-481-4471-6. In iCloud. Gives very nice historical review of electrodynamics and how it differs from Maxwell theory. Essentially instantaneous action at a distance without fields. Helmholtz and Weber were enemies. Also derived with Kirchhoff telegraph equation without displacement current and speed of light.
• F.J. Dyson, Feynman's proof of Maxwell's equations, American Journal of Physics 58, 209-211(1990) is somewhat related to this. On Berliner Schreibtisch.
• O. Darrigol, Electrodynamics from Ampère to Einstein, Oxford University Press, Oxford (2000). ISBN 0-19-850593-0. The whole story!! Discusses in detail Ampere's and Biot-Savart's experiments.
• D.J. Griffiths and M.A. Heald, Time‐dependent generalizations of the Biot–Savart and Coulomb laws, American Journal of Physics 59, 111-117(1991). On Berliner Schreibtisch.
• Engelsk WP, History of electromagnetic theory, much details.
• Engelsk WP, Fluid theory of electricity, much details.
• Thomas L. Hankins, Science and the Enlightenment, Cambridge University Press, Cambridge (1995). ISBN 978-0-521-28619-0, with more details and much about others.
• J.L. Heilbron, Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics, very long and detailed.
• Chemical Heritage Foundation, Joseph Priestley, Radical Thinker, biography in great detail.
• Encyclopedia.com, John Michell bio
• Physics News, APS, John Michell and some of his physics.
• Princeton, Oersted's theory of magnetism
• Princeton, Ampere's theory of magnetism
• Princeton, Telegraph history including link to book from 1837 giving full history, also of electricity in general.

• English WP, Uehling potential

Også fra flere ladninger. Trenger å utvide Elektrisk felt. Elektrostatisk feltenergi er utledet i engelsk WP Electrostatics. Elektrisk felt historisk sett diskutert i engelsk WP Electricity. Statisk elektrisitet godt beskrevet i engelsk WP Electrostatics som inneholder mange fine artikler. Kan benyttes til omskrivning av Statisk elektrisitet. In discussion here is also dealt with difference between static electricity and electrostatics.

• Book, Biot-Savarts lov utledet fra Special Relativity of moving charge.

• English WP, Classical EM and SR, with transformation formulas. Or Relativistic Electromagnetism with less math. For MIT students a la Feynman. Or for Cambridge students.

• U Delaware, Lectures on EM and SR, graphically very nice. On Berliner Schreibtisch.

Selve field-konseptet oppstod allerede fra Newton's behanding av grav. vekselvirkning fra sol og flere planeter hvor det var enklere å tilskrive disse et felt som virket i hvert punkt.

• Utvid Coulombs lov, fjern omdirigering fra Elektrostatikk og ta noe av stoffet fra Statisk elektrisitet.
• Utvid Coulombs lov i tråd med en:Coulomb's law og en:electrostatics

• J.L. Heilbron, Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics, University California Press, Berkeley (1979).ISBN 0-520-03478-3.
• APS News, Discovery Coulomb Law.
• S.Weinberg, The Search for Unity: Notes for a History of Quantum Field Theory, Daedalus, 106 (4), 17-35 (1977). On Berliner Schreibtisch.
• English WP, Newton's Shell Theorem w/derivations. Even better on Italian and Dutsch versions!!
• NN, Derivation of Shell Theorem
• R. Borghi, On Newton's shell theorem, European Journal of Physics 35, 028003 (2014). With ref. to book by Chandrasekhar about Newton's Principe for laymen.
• R. Fitzpatrick, U Texas, Coulomb's Law with vector notation.
• NN, Priestley contribution to Coulombs law
• Blog, Cavendish and Coulomb Law, very interesting!
• Stackexchange, Newton proposed first Coulomb's Law?
• NN, Some historical background
• NN, Electric forces on moving charges - basics
• Encyclopedia Britannicas, Coulomb's Law as stated by him.
• English WP, Breit interaction
• Köln, Relativistic corrections to Coulomb
• Harvard, Magnetic field from moving charges, on Berliner Schreibtisch.
• NN, Elementary relative strengths between electric and magnetic forces
• French, History behind Biot-Savart's law

• Tysk WP, Elektromagnetische Masseinheiten. Meget nyttig er omregningstabell på tysk WP CGS Einheiten
• Engelsk Wp, Lorentz-Heaviside units, at the end extended to natural HL-units with c = 1.
• N.J. Carron, Babel of units, arxiv-1506.01951. Excellent
• Berkeley, Notes on units
• William Baylis, Electrodynamics: A Modern Geometric Approach, starting up with discussing units and especially natural HL-units with c = 1.
• Revolvy, Conversion between different units

• NN, History of constant, in great detail. Argues that it should be called only Euler-konstant.

For bevis ved direkte integrasjon, se Pollack & Stump book on EM, p.53. Purcell book on EM in Berkeley series has on p. 27, saying that the proof he finally published in 1686 had delayed his theory of gravitation with almost 20 years.

• S. Chandrasekhar, Newton's Principia for the Common Reader, with Newton's original proofs and discussions.
• C. Schmid, Newton's superb theorem: An elementary geometric proof, American Journal of Physics, Jan. (2012) Kopie auf Berliner Schreibtisch. With Newton's historical comments to its discovery.

Newton's "superb theorem" for the gravitational inverse-square-law force states that a spherically symmetric mass distribution attracts a body outside as if the entire mass were concentrated at the center. This theorem is crucial for Newton's comparison of the Moon's orbit with terrestrial gravity (the fall of an apple), which is evidence for the inverse-square-law. Newton's geometric proof in the Principia "must have left its readers in helpless wonder" according to S. Chandrasekhar and J.E. Littlewood. In this paper we give an elementary geometric proof, which is much simpler than Newton's geometric proof and more elementary than proofs using calculus.

Newton's superb theorem: An elementary geometric proof (PDF Download Available). Available from: https://www.researchgate.net/publication/221660870_Newton%27s_superb_theorem_An_elementary_geometric_proof [accessed Sep 29, 2017].

• English WP, Newton's Shell Theorem w/derivations. Even better on Italian and Dutsch versions!! French version is extremely short, pure geometry?
• NN, Derivation of Shell Theorem
• R. Borghi, On Newton's shell theorem, European Journal of Physics 35, 028003 (2014). With ref. to book by Chandrasekhar about Newton's Principe for laymen.

• Assis and Chaib, Ampère's Electrodynamics, with complete story.
• Engelsk WP, Force between magnets, with very nice figures
• Illinois, Magnetic fields in matter, excellent. In WikiWorks. Same stuff is well explained by Rochester, Magnetic fields in matter
• J. M. D. Coey, Magnetism and Magnetic Materials, check it out!

• S.J. Blundell, Magnetism: A Very short introduction, Oxford University Press, Oxford (2012). ISBN 978-0-19-960120-2. Very relevant as introduction.

Se Magnetisk felt og magnetisk krets, også magnetisme og Ørsteds lov. Det finnes allerede en side Lorentzkraft, men også Lorentz-kraft. Omgjœr denne omdirigering!

Kan begynne med som hos Whittaker pp. 86-90 som først gir resultatet til Biot-Savart fra høsten 1820. De målte kraften F = g B på en austral eller boreal magnetpol g med resultatet for magnetfeltet B fra lite strømelement I ds. Dette er dagens uttrykk!! Ampere omtrent samtidig (litt før, publisert senere) fant kraften mellom strømsløyfer. Kombinasjon av måleresultat pluss antagelsen at kraften mellom to stromelement skulle være rettet langs deres forbindelseslinje, brukte han til å utlede sin kraftlov. Men tilsynelatende forskjellig fra hva Biot-Savart fant. Men forskjellen ligger i et totalt differensial slik at for lukket strømsløyfe bidrar ikke. Og det var dette leddet eller omskrivningen som Grassmann senere gjorde og dermed etablerte dagens uttrykk. Dette er også forklart i boken til Assis on Weber Electrodynamics. Ved å starte med B-S lov på differensiell form, har også magnetfelt for charge moving ved constant (and small) velocity which is starting point on p. 190 for excellent book

• J.R. Reitz, F.J. Milford and R.W. Christy, Foundations of Electromagnetic Theory, 4th edition, Pearson Addison-Wesley, San Fransisco (2009). ISBN 0-321-58174-1. New version in Berlin, older in Oslo. This new edition contains nice section on superconductivity.

Field history from Assis book on Gauss-Weber electrodynamics in ICloud: Lagrange introduced scalar potential in gravity in 1777. In 1782 Laplace found his equation for this field, published in 1785. In 1811 Poisson introduced scalar potential in electrostatics and 1813 found his equation for this inside matter. In Appendix A of this book also history of magnetic force law F = qv×B, very complicated!! Correct form was first stated by Heaviside in 1889 - after Maxwell dead. Magnetic vector potential A was proposed by Franz Neumann in 1845.

In same book p.74 stated that it was Helmholtz who sorted out conservation of energy, and in 1847 introduced kinetic energy 1/2mv^2 instead of vis viva mv^2. Also detailed description of Ampere's law for magnetic forces. But his original force law was soon forgotten. Instead in 1845 came Grassmann's formulation which is the one we use today. Grassmann found this modern formulation as an exercize in using his antisymmetric vector product!

In force law F = qv×B it was a problem what velocity to use. Relative to ether? When particle in moving frame with same velocity, particle is at rest and no force? No, because in moving frame B-field is transformed to E = v×B and new force is F = q E is the same! See English WP Moving magnet and conductor problem.

Det finnes allerede en side magnetisk felt omdirigert til magnetisme. I tillegg også en om magnetisk moment og en om magnet. Her brukes en figur med jernfilspon som er den samme som på magnetisk felt. Derfor bytt ut på denne siste med bedre figur av stavmagnet som vist her.

Ampere considered forces between closed current loops. Thus found his force law. Biot-Savart measured force due to magnetic field from current acting on magnetic pole (tip of compass?) with force law F = q B where q is pole charge. Thus found there law for B. History outlined in article by Jackson and Okun:

• J.D. Jackson and L.B. Okun, Historical roots of gauge invariance, Reviews of Modern Physics 73, 663-680 (2001) discusses this history of magnetic forces and potentials in great detail!!!

See also some history here:

• Harry Varvoglis, History and Evolution of Concepts in Physics, for some details about these experiments.

• Mathpages, First speed of light, in sec.8.6 says that speed of light first obtained by Kirchhoff in 1848 from ratio of electromagnetic to electrostatic units. Then again in 1858 by B. Riemann who presented a theory based on the hypothesis that electromagnetic effects propagate at a fixed speed, and then deduced that this speed must equal the ratio of electromagnetic and electrostatic units, i.e., 1/c = \sqrt(\epsilon_0 \mu_0). This is web version of book by Kevin Brown : Reflections on Relativity which is very rich on interesting comments. For an explanation of how speed of light appears from such considerations, consult footnote on p.227 of Whittaker book. Here in connection with Weber and his problem in Hannover caused by Queen Victoria, also explained p.225 Fechner's proposal that current consists of two oppositely-moving streams of charges of opposite signs. On p.231 describes B. Riemann's theory from 1861 for the force between two moving charges. On pp.257-258 described how Kirchhoff derived telegraph equation and finding speed of light. On p.261-262 told what Helmholtz did to reconcile Weber theory with Ampere-Neumann.

• E.T. Whittaker, A History of the Theories of Aether and Electricity, Longman, Green and Co, London (1910). EXCELLENT

At the end of this section 8.3 there is discussion of Gauss' law for two moving charges. In 1835 (discovered after his death) wrote force law, but had problem. Changed slightly by his friend W. Weber in 1845 removing one term getting his own force law. It was used by Weber as the basis of his theory of electrodynamics published in 1846. Indeed this formula served as the basis for most theoretical studies of electromagnetism until it was finally superseded by Maxwell's theory beginning in the 1870s.

• D. Cahan, Science and Culture, book in Berlin with talks given by H. Contains also short, but good biography. One talk is geometry of 3-dim spherical space starting with sphere in 4-dim!

• Feynman lectures, Volume II with electric and magnetic fields.
• Canada, Lorentztransformations in EM
• UIUC, Lectures on transformations of charges and fields
• UIUC, History of Electromagnetism
• NN, Ampere and Biot-Savart forces laws and differences.
• IEEE, Ampere and Grassmann force laws and differences.
• Barbour, Ampere, Grassmann and Weber forces and Mach Principle.
• NN, How to calculate inductance?
• Kjell Prydz, Electrodynamics: The Field-Free Approach: Electrostatics, Magnetism ...
• U. Lund, Discussion of different force laws, many webpages.
• U. Stockholm, Different force laws

I artikkelen om elektrisitet er Charles du Fay er beskrevet utførlig. Mer historie kan finnes i Encyclopedia Britannica 11th ed 1911 under electricity.

• Engelsk WP, History of electromagnetic theory, much details.
• Engelsk WP, Fluid theory of electricity, much details.
• Thomas L. Hankins, Science and the Enlightenment, Cambridge University Press, Cambridge (1995). ISBN 978-0-521-28619-0, with more details and much about others.
• J.L. Heilbron, Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics, very long and detailed.
• Chemical Heritage Foundation, Joseph Priestley, Radical Thinker, biography in great detail.
• Encyclopedia.com, John Michell bio
• Physics News, APS, John Michell and some of his physics.
• Princeton, Oersted's theory of magnetism
• Princeton, Ampere's theory of magnetism
• Princeton, Telegraph history including link to book from 1837 giving full history, also of electricity in general.

Finstruktur finnes allerede på no. Passende diskusjon i Alonso-Finn, Vol III, p.141. På side 131 også ok innføring til relativistisk korreksjon.

• Skriv ny side om covariante/contravariante komponenter: Basics lecture
• Mer generell fremstilling her Normal basis tangent vectors to coordinate curves, dual basis normals to coordinate planes hvor også figurer kan benyttes.

• Alexander Graham Bell bør forbedres. Hva som der stå om vannsendere virker forvirrende. Bedre forklart på engelsk WP, Water microphone