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2020-05-28

Maxwell's Derivation of the Lorentz Force from Faraday's Law

By Arthur Yaghjian
Progress In Electromagnetics Research M, Vol. 93, 35-42, 2020
doi:10.2528/PIERM20040202

Abstract

In a brief but brilliant derivation that can be found in Maxwell's Treatise and traced back to his 1861 and 1865 papers, he derives the force on a moving electric charge subject to electromagnetic fields from his mathematical expression of Faraday's law for a moving circuit. Maxwell's derivation in his Treatise of this force, which is usually referred to today as the Lorentz force, is given in detail in the present paper using Maxwell's same procedure but with more modern notation.

Citation


Arthur Yaghjian, "Maxwell's Derivation of the Lorentz Force from Faraday's Law," Progress In Electromagnetics Research M, Vol. 93, 35-42, 2020.
doi:10.2528/PIERM20040202
http://jpier.org/PIERM/pier.php?paper=20040202

References


    1. Maxwell, J. C., A Treatise on Electricity and Magnetism, 3rd Ed., Dover, New York, 1954. The Dover edition is an unabridged, slightly altered, republication of the third edition, published by the Clarendon Press in 1891. All additions to the Treatise made by W. D. Niven and J. J. Thomson are ignored in [2] and in the present paper so as to concentrate on Maxwell's original contributions.

    2. Yaghjian, A. D., "Reflections on Maxwell's Treatise," Progress In Electromagnetics Research, Vol. 149, 217-249, 2014; see also ``An overview of Maxwell's Treatise,'' FERMAT, Vol. 11, Sept.-Oct. 2015.
    doi:10.2528/PIER14092503

    3. Heaviside, O., "On the electromagnetic effects due to the motion of electrification through a dielectric," Phil. Mag. and J. Sci., fifth series, Vol. 27, 324-339, 1889.

    4. Lorentz, H. A., "La théorie électromagnétique de Maxwell et son application aux corps mouvants," Archives Néerlandaises des Sciences Exactes et Naturelles, Vol. 25, 363-552, 1892.

    5. Buchwald, J. D., From Maxwell to Microphysics, University of Chicago Press, Chicago, 1985.

    6. Faraday, M., Experimental Researches in Electricity, Dover, New York, 2004. Originally published in three volumes by J. E. Taylor, 1839-1855, London.

    7. Redžić, D. V., "Maxwell's inductions from Faraday's induction law," Eur. J. Phys., Vol. 39, 025205 (16pp), February 2018.

    8. Maxwell, J. C., "On physical lines of force, Part 2," Phil. Mag. and J. Sci., fourth series, Vol. 21, 282-349, March 1861.

    9. Maxwell, J. C., "A dynamical theory of the electromagnetic field," Phil. Trans. Roy. Soc. Lond., Vol. 155, 459-512, 1865.
    doi:10.1098/rstl.1865.0008

    10. Bucci, O. M., "The genesis of Maxwell's equations," History of Wireless, Ch. 4, Wiley, Hoboken, NJ, 2006.

    11. Maxwell, J. C., "On Faraday's lines of force," Trans. Cambridge Phil. Soc., Vol. 10, 27-83, 1856.

    12. Tai, C.-T., Generalized Vector and Dyadic Analysis, IEEE/Wiley, New York, 1997.
    doi:10.1109/9780470544754

    13. Yaghjian, A. D., "Maxwell's definition of electric polarization as displacement," Progress In Electromagnetics Research M, Vol. 88, 67-71, 2020.
    doi:10.2528/PIERM19090802

    14. Hertz, H., "Über sehr schnelle electrische Schwingungen,", plus two other papers, Annalen der Physik, Vol. 31, new series, 421-448; 543-544; 983-1000, 1887.

    15. Poynting, J. H., "On the transfer of energy in the electromagnetic field," Phil. Trans. Roy. Soc. Lond., Vol. 175, 343-361, January 1884.

    16. Yaghjian, A. D., "Classical power and energy relations for macroscopic dipolar continua derived from the microscopic Maxwell equations," Progress In Electromagnetics Research B, Vol. 71, 1-37, 2016.
    doi:10.2528/PIERB16081901