2020-01-04
Maxwell's Definition of Electric Polarization as Displacement
By
Progress In Electromagnetics Research M, Vol. 88, 65-71, 2020
Abstract
After reaffirming that the macroscopic dipolar electromagnetic equations, which today are commonly referred to as Maxwell's equations, are found in Maxwell's Treatise, we explain from his Treatise that Maxwell defined his displacement vector D as the electric polarization and did not introduce in his Treatise or papers the concept of electric polarization P or the associated electric-polarization volume and surface charge densities, -n.P and n.P, respectively. With this realization, we show that Maxwell's discussion of surface charge density between volume elements of dielectrics and between dielectrics and conductors becomes understandable and valid within the context of his definition of electric polarization as displacement D. Apparently, this identification of D with electric polarization in Maxwell's work has not been previously pointed out or documented except very briefly in [2].
Citation
Arthur D. Yaghjian, "Maxwell's Definition of Electric Polarization as Displacement," Progress In Electromagnetics Research M, Vol. 88, 65-71, 2020.
doi:10.2528/PIERM19090802
References

1. Maxwell, J. C., A Treatise on Electricity and Magnetism, 3rd Edition, Dover, New York, 1954.

2. Yaghjian, A. D., "Reflections on Maxwell’s Treatise," Progress In Electromagnetics Research, Vol. 149, 217-249, 2014.
doi:10.2528/PIER14092503        Google Scholar

3. Maxwell, J. C., "On Faraday’s lines of force," Trans. Cambridge Phil. Soc., Vol. 10, 27-83, 1856.        Google Scholar

4. Buchwald, J. Z., From Maxwell to Microphysics, University of Chicago Press, Chicago, 1985.

5. Sarkar, T. K., et al. History of Wireless, Wiley, Hoboken, NJ, 2006.
doi:10.1002/0471783021

6. Stratton, J. A., Electromagnetic Theory, McGraw-Hill, New York, 1941.

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

8. Yaghjian, A. D., "Maxwell’s derivation of the Lorentz force from Faraday’s law,", arXiv:1911.04605, November 2019.        Google Scholar

9. Thomson, W., "A mathematical theory of magnetism," Phil. Trans. Roy. Soc. Lond., Vol. 141, 269-285, January 1851.        Google Scholar

10. Faraday, M., Experimental Researches in Electricity, Dover, New York, 2004.

11. Maxwell, J. C., "A dynamical theory of the electromagnetic field," Phil. Trans. Roy. Soc. Lond., Vol. 155, 459-512, 1865.        Google Scholar

12. Larmor, J., "A dynamical theory of the electric and luminiferous medium — Part II. Theory of electrons," Phil. Trans. Roy. Soc. London (A), Vol. 186, 695-743, 1895.        Google Scholar

13. Leathem, J. G., "On the theory of the magneto-optic phenomena of iron, nickel, and cobalt," Phil. Trans. Roy. Soc. London (A), Vol. 190, 89-127, 1897.        Google Scholar

14. Lorentz, H. A., "The fundamental equations for electromagnetic phenomena in ponderable bodies deduced from the theory of electrons," Proc. Roy. Acad. Amsterdam, Vol. 5, 254-266, September 1902.        Google Scholar

15. Hansen, T. B. and A. D. Yaghjian, Plane-Wave Theory of Time-domain Fields: Near-field Scanning Applications, IEEE/Wiley, New York, 1999.
doi:10.1109/9780470545522