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Kilder naturlige enheter

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Dimensjonsanalyse

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Referanser

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More

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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

Eksterne lenker

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Kilder Charles Wheatstone

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Magnetisk konstant

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Permittivitet

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Rayleigh-spredning

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Sky polarization

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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

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.


Eksterne lenker

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Kilder elektroskop/elektrometer

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Maxwell og galvanometer

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Ohm standard

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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.

Elektromagnetisme rundt ledninger

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Telegrafligning

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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

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
  • 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

Kilder Fleeming Jenkin

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  • 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.

Kilder MKS-system

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Giorgo-systemet

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Kilder enhetssystem

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HEP units
  • 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

Kilder gaussiske enheter

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Kilder målesystem

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

Målesystem

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CGS-systemet

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Naturlige enheter

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British Science Association

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Electromagnetic units

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  • 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

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Skjema for en Tesla-transformator med primær - og sekundærspole.

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.

Virkemåte

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text

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

Bilder

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

Referanser

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  1. ^ C. Wheatstone, An Account of Some Experiments to Measure the Velocity of Electricity and the Duration of Electric Light, Philosophical Transactions of the Royal Society of London. 124, 583–591 (1837).
  2. ^ J.R. Reitz, F.J. Milford and R.W. Christy, Foundations of Electromagnetic Theory, Addison-Wesley, San Fransisco (1993). ISBN 0-321-58174-1.
  3. ^ T.K. Sarkar et al., History of Wireless, Wiley-Interscience, New York (2006). ISBN 978-0-471-71814-7.
  4. ^ M. Raboy, The Man Who Networked the World, Oxford University Press, New York (2016). ISBN 978-0-1993-13587.

Heinrich Hertz

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Sources early radio

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  • 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

Superheterodyne

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  • 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).

Poulsen-sender

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Kilder gnistsender

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Kilder for Sørvågen

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

Kilder Oliver Lodge

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Kilder elektriske svingninger

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Relativitetsteori

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Standard configuration of coordinate systems, fra engelsk WP, Galilean transformations.

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

Gammel versjon

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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.

Kilder til relativitet

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Eksterne lenker

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  • 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.

Litteratur for aberrasjon

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Relativitetsteori

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text
Todimensjonal projeksjon av en tredimensjonal analogi av krummingen av romtiden som beskrevet i den generelle relativitetsteorien.

Relativitetsprinsipp

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Text

Eter

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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 n 2 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/n 2 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

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,

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

Relativitet og EM

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  • 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.

Lorentz-kraften

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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

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.

EM Units

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Kjedelinje

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Electric Grids

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Elektrodynamikk

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Darwin-vekselvirkning

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Feynman-diagram.
  • 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

Referanser

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  1. ^ H.D. Young and R.A. Freedman, University Physics, Addison-Wesley, New York (2008). ISBN 978-0-321-50130-1.
  2. ^ M.L. Boas, Mathematical Methods in the Physical Sciences, John Wiley & Sons, New York (1983). ISBN 0-471-04409-1.
  3. ^ H. Goldstein, Classical Mechanics, Addidon-Wesley Publishing Company, Reading, Massachusetts (1959).
  4. ^ H. Goldstine: A History of the Calculus of Variations from the 17th through the 19th Century, Springer, New York (1980). ISBN 1-4613-8106-8.
  5. ^ L. N. Hand and J. D. Finch, Analytical Mechanics, Cambridge University Press, England (1998). ISBN 0-5215-7572-9

Relativistisk invarians

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Kovariant Maxwell-teori

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  • 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.

Webers elektrodynamikk kilder

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  • 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

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.

Lorentz-transformasjoner

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

Electrodynamic sources

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Tysk WP Elektrodynamik

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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.

Hva som kommer

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  • 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

Larmor litteratur

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

Radio og antenner

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Circuit diagram of a simple crystal radio.
Pictorial diagram from 1922 showing the circuit of a crystal radio. This common circuit did not use a tuning capacitor, but used the capacitance of the antenna to form the tuned circuit with the coil. The detector was a cat whisker detector, consisting of a piece of galena with a thin wire in contact with it on a part of the crystal, making a diode contact
Het ontvangen van een radiogolf met een dipoolantenne
En elektromagnetisk bølge inneholder elektriske E og magnetiske B felt som står vertikalt på utbredelsesretningen v.

Hertz dipol radiation

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EM stråling

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Magnetiske feltlinjer i strålingssonen utenfor en oscillerende, magnetisk dipol.

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/r 2 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

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

og analogt for alle andre Fourier-komponenter.

Magnetisk felt

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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

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

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

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

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

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.

Elektrisk felt

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Det elektriske feltet er generelt gitt ved de elektromagnetiske potensialene som

Her kan det skalare potensialet Φ finnes fra Lorenz-betingelsen

For de tilsvarende Fourier-komponentene har man dermed sammenhengen

Dermed blir

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]

Utstrålt energi

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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

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

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

På denne måten kan man definere en frekvens og retningsavhengig strålingsintensitet

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

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]

Kenmerken van het elektromagnetisch spectrum

Referanser

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  1. ^ a b c J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, New York (1998). ISBN 0-4713-0932-X.
  2. ^ W.K.H. Panoofsky and M. Phillips, Classical Electricity and Magnetism, Addison-Wesley, Reading, Massachusetts (1962).
  3. ^ G.L. Pollack and D.R.Stump, Electromagnetism, Pearson Education, San Francisco (2002). ISBN 0-8053-8567-3.

Elektrodynamikk

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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 Aμ 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 Fμν = ∂μAν - ∂νAμ med komponenter som er det elektriske feltet E og magnetiske feltet B. Samtidig er både Aμ og Fμν  felt ut fra den mer matematiske definisjonen av hva et felt er.

Larmor elektrodynamikk

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Tidligere elektrodynamikk

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Zeitliche Änderungen des magnetischen Flusses
  • 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.

Amperes kraftlov sources

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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.

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

Vakumda iki sonsuz paralel keçirici.


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.

Eksterne lenker

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Klassisk feltteori

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Spenninger

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Biot-Savart historie

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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 = ?

  • 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.

Flukskvantisering

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Fluksen gjennom flaten er et mål for antall feltlinjer som går gjennom den.

Eksterne lenker

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Referanser

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  1. ^ 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).

Feynman

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  • 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

Referanser

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  • Sørensen foto fra Grøn: Robert G. Berntsen

Se også

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Eksterne lenker

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Biot-Savarts lov

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  • 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.
Vakumda iki sonsuz paralel keçirici.

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

The magnetic field lines (green) of a current-carrying loop of wire pass through the center of the loop, concentrating the field there
Høyrehåndsregel current flowing in the direction of the white arrow produces a magnetic field shown by the red arrows.

Sources radiation pressure

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

Magnetisering

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Magnetiseringen i en stavmagnet har retning fra sydpol S til nordpol N.

EM forces and sources

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

Lorentzkraft eller Lorentz-kraft? Syklotron og syklotronfrekvens.

Hall-effekt

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Indian EM textbook

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Faradays induksjonslov

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Gauss's law for magnetism says that magnetic field lines never begin nor end
Discul lui Farday, inventat de Michael Faraday în 1831, unul dintre primele generatoare de curent și care ilustrează practic legea enunțată de marele fizician, fra romansk WP

Magnetic sources

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Biot'n ja Savartin lain mukaan johtimessa kulkeva sähkövirta I synnyttää johtimen ympärille magneettikentän B.
Magneettivuon tiheys pisteessä
-Feld eines geraden Leiters
Campo de uma espira circular
Right-hand rule for a current-carrying wire in a magnetic field B

Vortex atoms

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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.)

Magnetic sources

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Magnetiske material

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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.

Ørsted

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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.

Ampères strømmer

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

Historie - magnetisme

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A sketch of Earth's magnetic field representing the source of the field as a magnet. The geographic north pole of Earth is near the top of the diagram, the south pole near the bottom. The south pole of that magnet is deep in Earth's interior below Earth's North Magnetic Pole.

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

William Gilbert, De Magnete
An illustration from Gilbert's 1600 De Magnete showing one of the earliest methods of making a magnet. A blacksmith holds a piece of red-hot iron in a north-south direction and hammers it as it cools. The magnetic field of the Earth aligns the domains, leaving the iron a weak magnet.

Lord Kelvin (Thomson)

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Måtte innføre B og H.

Faraday og Maxwell

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Faraday-rotasjon

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Referanser

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Magnetostatikk # # # #

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  • 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
So in static case this gives from . In dynamic case can use eq. of continuity with harmonic time variation to get with total dipole moment .
  • 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.

Ferromagnetiske materialer

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

Einstein–de Haas-effekt

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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:

Termodynamikk med B og H

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Elektromagnetisme

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

Fjernvirkningsteori = Action at a distance

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  • 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.

Magnetiske felt

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Eksempel på en spole.
Magnetfeld einer Spule
Magnetisk felt rundt ein spole.
Field and density created by a solenoid with surface current density From English WP solenoid.
Magnetfelt skapt av en stavmagnet.
Del av magnetfältet runt en ledare
Field from a perfect dipole, both electric or magnetic.

Magnetisme

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Magnetiske kraftlinjer fra en stavmagnet vist med jernspon på et papirark
Photo d'un aimant lévitant au-dessus d'un supraconducteur.
Beeinflussung des Verlaufs der magnetischen Feldlinien durch ferromagnetisches Material. Innerhalb des Rings kommt es durch Abschirmung zu einem nahezu feldfreien Raum.

Birkeland elektromagnetisk kanon

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eller spolekanon.

Magnetostatikk

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Bruk av grensebetingelser bestemmer inntrengning i materiale
Magnetisk felt fra punktdipol

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

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.

Magnetiske kilder

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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.

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.
Magnetisk felt i kort solenoide

Ferromagnetisme

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Caratteristico allineamento ordinato dei dipoli magnetici in presenza di un campo magnetico esterno.

Ferromagnetisme finnes allerede i stub utgave.

Electron

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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.

Magnetisk monopol

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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.

Maxwells spenningstensor

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Greens funksjon

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Multipolutvikling

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Example of a quadrupole field. This can also be constructed by moving two dipoles together.

Eksterne kilder

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Hydrodynamikk

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Laplace-ligning

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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.

Poisson equation literature

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  • 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.

Hydrodynamisk litteratur

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Bain - History of Light

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Sources

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Eter

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

Eksterne lenker

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  1. # # # # # #
  • 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.

Elektriske kilder

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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.

Gauss' lov

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Electric field lines emanating from a point positive electric charge suspended over an infinite sheet of conducting material.
  • Det integrerade flödet är proportionellt mot de inneslutna källornas styrka.
    Det integrerade flödet är proportionellt mot de inneslutna källornas styrka.
  • Utan källor eller sänkor är det integrerade flödet noll.
    Utan källor eller sänkor är det integrerade flödet noll.
  • Flödets ytintegral för en dipol är noll.
    Flödets ytintegral för en dipol är noll.
Blau: E-Vektoren der negativen Platte.
Rot: E-Vektoren der positiven Platte

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.

Multipolutvikling

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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!

Innhold

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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!

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.

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.

Nahwirkung statt Fernwirkung: Tysk elektrisk felt

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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.

Bakgrunn målenheter og finstruktur

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Ledende kule i elektrisk felt
Elektriske feltlinjer fra en positiv punktladning.

Elektrisk feltlinjer

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.

Elektrostatikk

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Field lines in capacitor with fringe fields.
  • 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!

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.

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

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.

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.

Sources

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Målesystem

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Euler-Mascheroni-konstant

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Newtons skallteorem

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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].

Magnetisk felt

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Magnetisk felt langs aksen til en kort, strømførende spole.
Illustrasjon fra De Magnete (Gilbert, 1600) av retningen til en kompassnål forskjellige steder på jordkloden med Nordpolen til høyre. BRUKT på magnetisme.
Magnetfelt utenfor en stavmagnet. BRUKT på magnetisme.

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.

History

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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:

  • 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.

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.

Hermann von Helmholtz

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  • 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!

Magnetic sources

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Elektrisitet

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Campo elettrostatico per una carica puntiforme nello spazio

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

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

Telefon

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