Scalar Wave Driven Energy Applications pp 123-176 | Cite as

# Maxwell’s Equations—Generalization of Ampère-Maxwell’s Law

## Abstract

Ampère’s Law, relating a steady electric current to a circulating magnetic field, was well known by the time James Clerk Maxwell started his research in a similar field in the 1850s. Although Ampère’s Law was known to apply only to static situations involving steady currents, it was Maxwell’s effort to add another source term—a change of electric flux—that extended the applicability of Ampère’s Law to time-dependent conditions. More important, it was the presence of this term in Ampère’s equation that led to it being known as Ampère-Maxwell’s Law. It allowed Maxwell to distinguish the electromagnetic nature of light and to develop a comprehensive theory of electromagnetism [1].

## References

- 1.D. Fleisch,
*A Student’s Guide to Maxwell’s Equations*, 1st edn. (Cambridge: Cambridge University Press, New York, 2008)Google Scholar - 2.J.R. Reitz, F.J. Milford, R.W. Christy,
*Foundations of Electromagnetic Theory*, 3rd edn. (Reading, MA: Addison – Wesley Publishing, New York, 1979)Google Scholar - 3.J. Peatross, M. Ware,
*Physics of Light and Optics*(Brigham Young University, March 16, 2015 Edition, New York)Google Scholar - 4.J.D. Jackson,
*Classical Electrodynamics*, 3rd edn. (New York: John Wiley Publisher, 1990), pp. 27–29Google Scholar - 5.W.H. Furry,
*Examples of Momentum Distributions in the Electromagnetic Field and in Matter, Am. J. Phys.***37**, 621 (1969)Google Scholar - 6.L.D. Landau, E.M. Lifshitz,
*The Classical Theory of Fluids*, Third Revised English Edition. (Boston: Pergamon Press, Addison-Wesley Publishing, New York, 1971)Google Scholar - 7.A. Einstein et al.,
*The Principle of Relativity*(Mineola, Dover Publications, 1923), Chapter VGoogle Scholar - 8.D. Griffiths,
*Introduction to Electrodynamics*, 3rd edn (Upper Saddle River: Prentice Hall, New York, 1999)Google Scholar - 9.R. Fitzpatrick,
*Maxwell’s Equations and the Principles of Electromagnetism*(Sudbury, MA: Infinity Science Press LLC, New York, 2008)Google Scholar - 10.A. Steane,
*Relativity Made Relatively Easy*, 1 edn. (Oxford: Oxford University Press, New York, December 1, 2012)Google Scholar