- Title Pages
- Preface
- Contents
- 1 Some essential mathematics
- 2 Static electric fields in vacuum
- 3 The electrostatics of conductors
- 4 Static magnetic fields in vacuum
- 5 Quasi-static electric and magnetic fields in vacuum
- 6 Ohm’s law and electric circuits
- 7 Electromagnetic fields and waves in vacuum
- 8 The electromagnetic potentials
- 9 Static electric and magnetic fields in matter
- 10 Some applications of Maxwell’s equations in matter
- 11 Electromagnetic radiation
- 12 Electromagnetism and special relativity
- Appendix A Vectors and Cartesian tensors
- Appendix A Vectors and Cartesian tensors
- Appendix B Cartesian coordinates
- Appendix C Spherical polar coordinates
- Appendix D Cylindrical polar coordinates
- Appendix E The Dirac delta function
- Appendix E The Dirac delta function
- Appendix F Legendre polynomials
- Appendix F Legendre polynomials
- Appendix G Bessel functions
- Appendix G Bessel functions
- Appendix H Parametric representation of a surface
- Appendix H Parametric representation of a surface
- Appendix I The Cauchy–Riemann equations
- Appendix I The Cauchy–Riemann equations
- Appendix J Questions involving computational work
- Glossary of symbols
- Index

# Electromagnetic fields and waves in vacuum

# Electromagnetic fields and waves in vacuum

- Chapter:
- (p.334) 7 Electromagnetic fields and waves in vacuum
- Source:
- Solved Problems in Classical Electromagnetism
- Author(s):
### J. Pierrus

- Publisher:
- 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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- Title Pages
- Preface
- Contents
- 1 Some essential mathematics
- 2 Static electric fields in vacuum
- 3 The electrostatics of conductors
- 4 Static magnetic fields in vacuum
- 5 Quasi-static electric and magnetic fields in vacuum
- 6 Ohm’s law and electric circuits
- 7 Electromagnetic fields and waves in vacuum
- 8 The electromagnetic potentials
- 9 Static electric and magnetic fields in matter
- 10 Some applications of Maxwell’s equations in matter
- 11 Electromagnetic radiation
- 12 Electromagnetism and special relativity
- Appendix A Vectors and Cartesian tensors
- Appendix A Vectors and Cartesian tensors
- Appendix B Cartesian coordinates
- Appendix C Spherical polar coordinates
- Appendix D Cylindrical polar coordinates
- Appendix E The Dirac delta function
- Appendix E The Dirac delta function
- Appendix F Legendre polynomials
- Appendix F Legendre polynomials
- Appendix G Bessel functions
- Appendix G Bessel functions
- Appendix H Parametric representation of a surface
- Appendix H Parametric representation of a surface
- Appendix I The Cauchy–Riemann equations
- Appendix I The Cauchy–Riemann equations
- Appendix J Questions involving computational work
- Glossary of symbols
- Index