Abstract
In Chap. 10 we obtained the full Maxwell Equations in the presence of charges and currents as sources. And in Chap. 1 Sect. 1.12.1 we encountered the experiments of Hertz, which identified the electromagnetic waves predicted by Maxwell. In this chapter we will solve Maxwell’s Equations in free space, without the presence of charges or currents as sources. This solution will provide us with a detailed picture of the structure of the electromagnetic waves that are possible in the context of classical electromagnetic field theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A proof of this property of partial derivatives may be found in any text on multivariate calculus (e.g. [15], volume II, pp. 55–56).
- 2.
Functions satisfying Maxwell’s Equations must have continuous first derivatives and those satisfying the wave equation must have continuous second derivatives.
- 3.
This is a specific form of the general requirement for the completeness of a set of continuous vectors first proven by Dirac [21].
- 4.
Jean-Baptiste le Rond d’Alembert (1717–1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Helrich, C.S. (2012). Electromagnetic Waves. In: The Classical Theory of Fields. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23205-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-23205-3_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23204-6
Online ISBN: 978-3-642-23205-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)