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Solved Problems in Classical ElectromagnetismAnalytical and Numerical Solutions with Comments$
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J. Pierrus

Print publication date: 2018

Print ISBN-13: 9780198821915

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198821915.001.0001

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Electromagnetic fields and waves in vacuum

Electromagnetic fields and waves in vacuum

(p.334) 7 Electromagnetic fields and waves in vacuum
Solved Problems in Classical Electromagnetism

J. Pierrus

Oxford University Press

In previous chapters four experimental laws of electromagnetism were encountered: Gauss’s law in electrostatics, Gauss’s law in magnetism, Faraday’s law and Ampere’s law. Now, in this chapter, these laws are generalized where appropriate to include the time-dependent charge and current densities ρ‎(r, t) and J(r, t) respectively. The result is a set of four coupled differential equations—known as Maxwell’s equations— which provide the foundation upon which the theory of classical electrodynamics is based. One of the most important aspects which emerges from Maxwell’s theory is the prediction of electromagnetic waves, and an entire spectrum of electromagnetic radiation. Some of the properties of these waves travelling in unbounded vacuum are considered, as well as their polarization states, energy and momentum conservation in the electromagnetic field and also applications to wave guides and transmission lines.

Keywords:   electromagnetic fields electromagnetic waves, continuity equation Maxwell’s equations, homogeneous wave equation plane waves, polarization Poynting vector, wave guides transmission line

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