Advertisement

Microscopic Potentials and Radiation

  • Kurt E. Oughstun
Chapter
  • 402 Downloads
Part of the Springer Series in Optical Sciences book series (SSOS, volume 224)

Abstract

The microscopic Maxwell equations consist of a set of coupled first-order partial differential equations relating the electric and magnetic field vectors that comprise the electromagnetic field to each other as well as to their charge and current sources. Their solution is often facilitated by the introduction of auxiliary fields known as potentials. These potentials have their origin in the two homogeneous equations ∇⋅b = 0 and ∇×e = −∥1∕cb∂t which indicate that not all of the components of the field vectors e and b are entirely independent.

References

  1. 1.
    E. T. Whittaker, A History of the Theories of the Aether and Electricity. London: T. Nelson & Sons, 1951.zbMATHGoogle Scholar
  2. 2.
    L. Lorenz, “On the identity of the vibrations of light with electrical currents,” Philos. Mag., vol. 34, pp. 287–301, 1867.CrossRefGoogle Scholar
  3. 3.
    J. V. Bladel, “Lorenz or Lorentz?,” IEEE Antennas Prop. Mag., vol. 33, p. 69, 1991.CrossRefGoogle Scholar
  4. 4.
    P. M. Morse and H. Feshbach, Methods of Theoretical Physics. New York: McGraw-Hill, 1953. Vol. I.Google Scholar
  5. 5.
    H. Hertz, “Die Kräfte electrischer Schwingungen, behandelt nach der Maxwell’schen Theorie,” Ann. Phys., vol. 36, pp. 1–22, 1889.CrossRefGoogle Scholar
  6. 6.
    A. Righi, “Electromagnetic fields,” Nuovo Cimento, vol. 2, pp. 104–121, 1901.CrossRefGoogle Scholar
  7. 7.
    A. Nisbet, “Hertzian electromagnetic potentials and associated gauge transformations,” Proc. Roy. Soc. A, vol. 231, pp. 250–263, 1955.ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Liénard, “Electric and magnetic field produced by a moving charged particle,” L’Éclairage Électrique, vol. 16, pp. 5–14, 53–59, 106–112, 1898.Google Scholar
  9. 9.
    E. Wiechert, “Electrodynamical laws,” Arch. Néerland., vol. 5, pp. 549–573, 1900.Google Scholar
  10. 10.
    W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism. Reading, MA: Addison-Wesley, 1955. Ch. 19–20.Google Scholar
  11. 11.
    J. M. Stone, Radiation and Optics, An Introduction to the Classical Theory. New York: McGraw-Hill, 1963.Google Scholar
  12. 12.
    E. T. Whittaker and G. N. Watson, Modern Analysis. London: Cambridge University Press, fourth ed., 1963. p. 133.Google Scholar
  13. 13.
    H. Hertz, Electric Waves. London: Macmillan, 1893. English translation.Google Scholar
  14. 14.
    H. S. Green and E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. A, vol. 66, no. 12, pp. 1129–1137, 1953.ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    E. Wolf, “A scalar representation of electromagnetic fields: III,” Proc. Phys. Soc., vol. 74, pp. 281–289, 1959.MathSciNetCrossRefGoogle Scholar
  16. 16.
    E. T. Whittaker, “On an expression of the electromagnetic field due to electrons by means of two scalar potential functions,” Proc. Lond. Math. Soc., vol. 1, pp. 367–372, 1904.MathSciNetCrossRefGoogle Scholar
  17. 17.
    P. Roman, “A scalar representation of electromagnetic fields: II,” Proc. Phys. Soc., vol. 74, pp. 269–280, 1959.MathSciNetCrossRefGoogle Scholar
  18. 18.
    A. Nisbet and E. Wolf, “On linearly polarized electromagnetic waves of arbitrary form,” Proc. Camb. Phil. Soc., vol. 50, pp. 614–622, 1954.ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    M. Born and E. Wolf, Principles of Optics. Cambridge: Cambridge University Press, seventh (expanded) ed., 1999.Google Scholar
  20. 20.
    H. Goldstein, Classical Mechanics. Reading: Addison-Wesley, 1950. Sections 1–5 and 11–5.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kurt E. Oughstun
    • 1
  1. 1.College of Engineering and Mathematical Sciences, University of VermontBurlingtonUSA

Personalised recommendations