Magnetomotorna sila

Magnetomotorna sila je sila koja proizvodi magnetsko polje kod elektromagneta.^[1]

Simbol je obično F_m a jedinica je amper-zavoj (amper-zavojak, amper-navoj ili amper-navojak), ustanovljena na bazi jačine struje u jednom zavoju žice. Pošto amper-zavoj nije SI definisana jedinica, često se jednostavno koristi Amper/metar.

Sljedeća formula iskazuje jačinu magnetomotorne sile:^[2]

\mathbf {F_{m}} =\mathbf {N} \mathbf {I}

gde je

$\mathbf {F_{m}}$ magnetomotorna sila u Amper-zavojima,
N broj zavoja, i
I struja u amperima.

Jačina magnetskog toka^[3]^[4] kroz neki materijal zavisi o jačini magnetomotorne sile i reluktansi materijala.^[5]^[6]^[7] To se može iskazati sljedećom jednačinom:

\mathbf {\Phi } ={\frac {F_{m}}{\mathcal {R}}}

Jedinice[uredi | uredi izvor]

SI jedinica za mmf je amper, isto kao i jedinica struje (analogno jedinici emf^[8]^[9]^[10] i napona volt). Neformalno, i često, ova jedinica se navodi kao amper-zavoj kako bi se izbegla zabuna sa strujom. Ovo je bio naziv jedinice u sistemu MKS. Povremeno se može sresti i cgs sistemska jedinica gilbert.^[11]

Istorija[uredi | uredi izvor]

Termin magnetomotorna sila je skovao Henri Ogastus Rovland 1880. godine.^[12]^[13]^[14] Rovland je nameravao da ovo ukaže na direktnu analogiju sa elektromotornom silom.^[15] Ideja o magnetnoj analogiji sa elektromotornom silom može se naći mnogo ranije u radu Majkla Faradaja (1791-1867), a nagovestio ju je u Džejms Klerk Maksvel (1831-1879). Međutim, Rovland je skovao taj termin i bio je prvi koji je eksplicitno naveo Omov zakon za magnetna kola 1873. godine.^[16]

Omov zakon za magnetna kola se ponekad naziva Hopkinsonovim zakonom, a ne Rovlandovim zakonom, jer neki autori pripisuju zakon Džonu Hopkinsonu umesto Roulandu.^[17] Prema pregledu metoda analize magnetnih kola, ovo je netačna atribucija koja potiče iz Hopkinsonovog rada iz 1885. godine.^[18] Štaviše, Hopkinson zapravo citira Rovlandov rad iz 1873. u ovom radu.^[19]

Primeri[uredi | uredi izvor]

Treba naći magnetomotornu silu elektromagneta sa N=5 navoja žice kroz koje prolazi struja od I=2 A.

$\mathbf {F_{m}} =\mathbf {N} \mathbf {I}$ = 5 zavoja • 2 A = 10 Amper-zavoja.

Ako pretpostavimo da je reluktansa magnetnog kola ${\mathcal {R}}$ = 40 000 Amper-zavoja/Wb, magnetski tok (fluks) kroz magnetsko kolo jest:

$\mathbf {\Phi } ={\frac {F_{m}}{\mathcal {R}}}$ = ${\frac {10}{40000}}$ = 250 μWb.

Vidi još[uredi | uredi izvor]

Reference[uredi | uredi izvor]

^ Waygood, str. 137
^ Smith, str. 495–506
^ Purcell, Edward; Morin, David (2013). Electricity and Magnetism (3rd izd.). New York: Cambridge University Press. str. 278. ISBN 978-1-107-01402-2.
^ Browne, Michael (2008). Physics for Engineering and Science (2nd izd.). McGraw-Hill/Schaum. str. 235. ISBN 978-0-07-161399-6.
^ Rowland, Henry A. (1873). „XIV. On magnetic permeability, and the maximum of magnetism of iron, steel, and nickel”. Philosophical Magazine. Series 4. 46 (304): 140—159. doi:10.1080/14786447308640912.
^ Rowland, Henry A, "On the general equations of electro-magnetic action, with application to a new theory of magnetic attractions, and to the theory of the magnetic rotation of the plane of polarization of light" (part 2), American Journal of Mathematics, vol. 3, nos. 1–2, pp. 89–113, March 1880.
^ Bosanquet, R.H.M. (1883). „XXVIII.On magnetomotive force”. Philosophical Magazine. Series 5. 15 (93): 205—217. doi:10.1080/14786448308628457.
^ Stewart, Joseph V. (2001). Intermediate electromagnetic theory. World Scientific. str. 389.
^ Tipler, Paul A. (januar 1976). Physics. New York, NY: Worth Publishers, Inc. str. 803. ISBN 978-0-87901-041-6.
^ Irving Langmuir (1916). „The Relation Between Contact Potentials and Electrochemical Action”. Transactions of the American Electrochemical Society. The Society. 29: 175.
^ Cardarelli, F. (2003). Encyclopaedia of Scientific Units, Weights and Measures. Their SI Equivalences and Origins.. London: Springer. str. 24. ISBN 978-1-4471-1122-1.
^ Cahan, David; Rudd, M. Eugene (2000). Science at the American Frontier: A Biography of DeWitt Bristol Brace. University of Nebraska Press. str. 22.
^ Buchwald, Jed Z. (1994). The Creation of Scientific Effects: Heinrich Hertz and Electric Waves. University of Chicago Press. str. 354.
^ Cahan, David (1993). Hermann von Helmholtz and the Foundations of Nineteenth-century Science. University of California Press. str. 397.
^
Hon & Goldstein, pp. 638-639
- Rowland (1880), pp. 92, 97
^
Thompson, p. viii
- Rowland (1873), p. 143
^
See for instance
- Schmidt & Schitter, p. 340, or
- Waygood, p. 137
^ Lambert et al., p. 2427
^ Hopkinson, str. 455

Literatura[uredi | uredi izvor]

Principles of Electric Circuits, 7th edition, Thomas I. Floyd, Prentice Hall. ISBN 978-0-13-098576-7. str. 386-387.
Hon, Giora; Goldstein, Bernard R, "Symmetry and asymmetry in electrodynamics from Rowland to Einstein", Studies in History and Philosophy of Modern Physics, vol. 37, iss. 4, pp. 635-660, Elsevier December 2006.
Hopkinson, John, "Magnetisation of iron", Philosophical Transactions of the Royal Society, vol. 176, pp. 455-469, 1885.
Lambert, Mathieu; Mahseredjian, Jean; Martínez-Duró, Manuel; Sirois, Frédéric, "Magnetic circuits within electric circuits: critical review of existing methods and new mutator implementations", IEEE Transactions on Power Delivery, vol. 30, iss. 6, pp. 2427-2434, December 2015.
Rowland, Henry A, "On magnetic permeability and the maximum magnetism of iron, steel, and nickel", Philosophical Magazine, series 4, vol. 46, no. 304, pp. 140-159, August 1873.
Rowland, Henry A, "On the general equations of electro-magnetic action, with application to a new theory of magnetic attractions, and to the theory of the magnetic rotation of the plane of polarization of light" (part 2), American Journal of Mathematics, vol. 3, nos. 1-2, pp. 89–113, March 1880.
Schmidt, Robert Munnig; Schitter, Georg, "Electromechanical actuators", ch. 5 in Schmidt, Robert Munnig; Schitter, Georg; Rankers, Adrian; van Eijk, Jan, The Design of High Performance Mechatronics, IOS Press, 2014 ISBN 1614993688.
Thompson, Silvanus Phillips, The Electromagnet and Electromagnetic Mechanism, Cambridge University Press, 2011 (first published 1891) ISBN 1108029213.
Smith, R.J. (1966), Circuits, Devices and Systems, Chapter 15, Wiley International Edition, New York. Library of Congress Catalog Card No. 66-17612
Waygood, Adrian, An Introduction to Electrical Science, Routledge, 2013 ISBN 1135071136.
The Penguin Dictionary of Physics, 1977, ISBN 0-14-051071-0
A Textbook of Electrical Technology, 2008, ISBN 81-219-2440-5
Rowland, H. A. (1878). „On the magnetic effect of electric convection”. American Journal of Science. 3rd series. 15: 30—38 — preko hathitrust.org.
Rowland, H. A. (1879). „Note on the magnetic effect of electric convection”. Philosophical Magazine. 5th series. 7: 442—443 — preko hathitrust.org.
Rowland, Henry A. (1878). „Research on the absolute unit of electrical resistance”. American Journal of Science. 3rd series. 15 (88): 281—291, 325—336, 430—439. Bibcode:1878AmJS...15..281R. S2CID 219243060. doi:10.2475/ajs.s3-15.88.281 — preko hathitrust.org.
David M. Cook (2003). The Theory of the Electromagnetic Field. Courier Dover. str. 157. ISBN 978-0-486-42567-2.
Lawrence M Lerner (1997). Physics for scientists and engineers. Jones & Bartlett Publishers. str. 724—727. ISBN 978-0-7637-0460-5.
„Electrolytic Cells”. hyperphysics.phy-astr.gsu.edu. Pristupljeno 17. 5. 2018.
„Electrochemical Cells”. hyperphysics.phy-astr.gsu.edu. Pristupljeno 17. 5. 2018. „Electrochemical cells which generate an electric current are called voltaic cells or galvanic cells, and common batteries consist of one or more such cells. In other electrochemical cells an externally supplied electric current is used to drive a chemical reaction which would not occur spontaneously. Such cells are called electrolytic cells.”
Brittain, J.E. (mart 1990). „Thevenin's theorem”. IEEE Spectrum. 27 (3): 42. doi:10.1109/6.48845. Pristupljeno 1. 2. 2013.
Dorf, Richard C.; Svoboda, James A. (2010). „Chapter 5 - Circuit Theorems”. Introduction to Electric Circuits (8th izd.). Hoboken, NJ: John Wiley & Sons. str. 162—207. ISBN 978-0-470-52157-1. Arhivirano iz originala 30. 4. 2012. g. Pristupljeno 16. 6. 2019.
Imaeda, K. (1995), „Biquaternionic Formulation of Maxwell's Equations and their Solutions”, Ur.: Ablamowicz, Rafał; Lounesto, Pertti, Clifford Algebras and Spinor Structures, Springer, str. 265—280, ISBN 978-90-481-4525-6, doi:10.1007/978-94-015-8422-7_16
On Faraday's Lines of Force – 1855/56. Maxwell's first paper (Part 1 & 2) – Compiled by Blaze Labs Research (PDF).
On Physical Lines of Force – 1861. Maxwell's 1861 paper describing magnetic lines of force – Predecessor to 1873 Treatise.
James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field", Philosophical Transactions of the Royal Society of London 155, 459–512 (1865). (This article accompanied a December 8, 1864 presentation by Maxwell to the Royal Society.)
A Dynamical Theory Of The Electromagnetic Field – 1865. Maxwell's 1865 paper describing his 20 equations, link from Google Books.
J. Clerk Maxwell (1873), "A Treatise on Electricity and Magnetism":
Maxwell, J. C., "A Treatise on Electricity And Magnetism" – Volume 1 – 1873 – Posner Memorial Collection – Carnegie Mellon University.
Maxwell, J. C., "A Treatise on Electricity And Magnetism" – Volume 2 – 1873 – Posner Memorial Collection – Carnegie Mellon University.
Larmor Joseph (1897). „On a dynamical theory of the electric and luminiferous medium. Part 3, Relations with material media”. Phil. Trans. R. Soc. 190: 205—300.
Lorentz Hendrik (1899). „Simplified theory of electrical and optical phenomena in moving systems”. Proc. Acad. Science Amsterdam. I: 427—443.
Lorentz Hendrik (1904). „Electromagnetic phenomena in a system moving with any velocity less than that of light”. Proc. Acad. Science Amsterdam. IV: 669—678.
Henri Poincaré (1905) "Sur la dynamique de l'électron", Comptes Rendus de l'Académie des Sciences, 140, 1504–1508.
Catt, Walton and Davidson. "The History of Displacement Current" Arhivirano 2008-05-06 na sajtu Wayback Machine. Wireless World, March 1979.

Spoljašnje veze[uredi | uredi izvor]

O magnetskom polju Arhivirano na sajtu Wayback Machine (3. jun 2011)

[1] Waygood, str. 137

[2] Smith, str. 495–506

[3] Purcell, Edward; Morin, David (2013). Electricity and Magnetism (3rd izd.). New York: Cambridge University Press. str. 278. ISBN 978-1-107-01402-2.

[4] Browne, Michael (2008). Physics for Engineering and Science (2nd izd.). McGraw-Hill/Schaum. str. 235. ISBN 978-0-07-161399-6.

[5] Rowland, Henry A. (1873). „XIV. On magnetic permeability, and the maximum of magnetism of iron, steel, and nickel”. Philosophical Magazine. Series 4. 46 (304): 140—159. doi:10.1080/14786447308640912.

[6] Rowland, Henry A, "On the general equations of electro-magnetic action, with application to a new theory of magnetic attractions, and to the theory of the magnetic rotation of the plane of polarization of light" (part 2), American Journal of Mathematics, vol. 3, nos. 1–2, pp. 89–113, March 1880.

[7] Bosanquet, R.H.M. (1883). „XXVIII.On magnetomotive force”. Philosophical Magazine. Series 5. 15 (93): 205—217. doi:10.1080/14786448308628457.

[Stewart-8] Stewart, Joseph V. (2001). Intermediate electromagnetic theory. World Scientific. str. 389.

[Tipler803-9] Tipler, Paul A. (januar 1976). Physics. New York, NY: Worth Publishers, Inc. str. 803. ISBN 978-0-87901-041-6.

[10] Irving Langmuir (1916). „The Relation Between Contact Potentials and Electrochemical Action”. Transactions of the American Electrochemical Society. The Society. 29: 175.

[:0-11] Cardarelli, F. (2003). Encyclopaedia of Scientific Units, Weights and Measures. Their SI Equivalences and Origins.. London: Springer. str. 24. ISBN 978-1-4471-1122-1.

[12] Cahan, David; Rudd, M. Eugene (2000). Science at the American Frontier: A Biography of DeWitt Bristol Brace. University of Nebraska Press. str. 22.

[13] Buchwald, Jed Z. (1994). The Creation of Scientific Effects: Heinrich Hertz and Electric Waves. University of Chicago Press. str. 354.

[14] Cahan, David (1993). Hermann von Helmholtz and the Foundations of Nineteenth-century Science. University of California Press. str. 397.

[15] Hon & Goldstein, pp. 638-639
Rowland (1880), pp. 92, 97

[16] Rowland (1880), pp. 92, 97

[16] Thompson, p. viii
Rowland (1873), p. 143

[18] Rowland (1873), p. 143

[17] See for instance
Schmidt & Schitter, p. 340, or
Waygood, p. 137

[20] Schmidt & Schitter, p. 340, or

[21] Waygood, p. 137

[18] Lambert et al., p. 2427

[19] Hopkinson, str. 455

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]