Vol. 93
Latest Volume
All Volumes
PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2020-05-28
Maxwell's Derivation of the Lorentz Force from Faraday's Law
By
Progress In Electromagnetics Research M, Vol. 93, 35-42, 2020
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://www.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