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.
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