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Essential Electrodynamics

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Language:  English
“Essential Electrodynamics” builds on “Essential Electromagnetism” and provides a concise introduction to this fundamental topic.
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“Essential Electrodynamics” builds on “Essential Electromagnetism” and provides a concise introduction to this fundamental topic. Starting with Maxwell's equations and conservation laws, it takes a logical step-by-step progression through electromagnetic waves in empty space, dispersive media and in waveguides. The book ends with radiation and scattering, initially using an heuristic approach to derive Larmor’s formula and applying it to simple problems. The book goes into sufficient detail to explain the important concepts using clear explanations, numerous diagrams, examples and problems.

“Essential Electrodynamics” and my previous book “Essential Electromagnetism” (also published by Ventus Publishing ApS) are intended to be resources for students taking electromagnetism courses while pursuing undergraduate studies in physics and engineering. Due to limited space available in this series, it is not possible to go into the material in great depth, so I have attempted to encapsulate what I consider to be the essentials. This book does not aim to replace existing textbooks on these topics of which there are many excellent examples, several of which are listed in the bibliography. Nevertheless, if appropriately supplemented, this book and my other book “Essential Electromagnetism” could together serve as a textbook for 2nd and 3rd year electromagnetism courses at Australian and British universities, or for junior/senior level electromagnetism courses at American universities/colleges.

The book assumes a working knowledge of partial differential equations, vectors and vector calculus as would normally be acquired in mathematics courses taken by physics and engineering students. It also assumes knowledge of electromagnetism at the level of “Essential Electromagnetism”, which also contains very brief introductions to vectors, vector calculus and index notation. Some of the mathematical derivations have been relegated to the appendices, and some of those are carried out using index notation, but elsewhere in the book manipulation of equations involving vector differential calculus is done using standard vector calculus identities given in the appendices.

“Essential Electrodynamics” starts with the electromotive force and Faraday’s law, the displacement current, Maxwell’s equations and conservation laws. It then discusses the wave equation, electromagnetic waves on lossless transmission lines, in empty space, and in linear dielectrics (including reflection and transmission at an interface). This is followed by electromagnetic waves in dispersive media including dielectrics, conductors and diffuse plasmas, as well as in waveguides. The book ends with radiation and scattering, using first an heuristic approach to derive Larmor’s formula, and then apply it to simple problems before taking up a more formal approach using the retarded potentials in the far zone to discuss antenna radiation.

Each chapter is followed by several exercise problems, and solutions to these problems are published separately by Ventus as “Essential Electrodynamics - Solutions”. I suggest you attempt these exercises before looking at the solutions.

I hope you find this book useful. If you find typos or errors I would appreciate you letting me know so that I can fix them in the next edition. Suggestions for improvement are also welcome – please email them to me at

I am grateful to thank Professors Anita Reimer and Todor Stanev for kindly reading a draft of the manuscript. However, all errors are entirely due to me. This book was mainly written in the evenings and I would like to thank my family for their support and forbearance.

This book is dedicated to the memory of my parents, who nurtured my interest in science.

Raymond John Protheroe,

School of Chemistry and Physics, The University of Adelaide, Australia

Adelaide, May 2013

  • Preface

  1. Electrodynamics and conservation laws
    1. Electro-motive force
    2. Maxwell’s equations
    3. Conservation of energy
    4. Conservation of momentum
  2. Electromagnetic waves in empty space and linear dielectrics
    1. The wave equation and its monochromatic plane wave solutions
    2. Transmission lines
    3. EM waves in vacuum and linear media
    4. Coherence of EM waves
    5. Polarisation of EM waves
    6. Reflection and transmission of EM waves at an interface between linear media
    7. Fresnel equations
  3. Electromagnetic waves in dispersive media
    1. Dispersion and absorption
    2. Dispersion
    3. Refractive index of a conductor
    4. Wave propagation in dilute plasmas
  4. Waveguides
    1. Waves in rectangular waveguides
    2. Waveguide modes
    3. Dispersion relation, phase and group velocities
    4. The EM field and power transmitted for TE10 mode
  5. Radiation and scattering
    1. Larmor’s formula
    2. Electric dipole radiation
    3. Scattering of EM radiation
    4. Formal treatment of radiation by charges and currents
    5. Antenna theory and multipole expansion in the far zone
    6. Radiation from quadrupole antennas
    7. Radiation from long antennas

  • Bibliography
  • Appendices
  • A: SI units and dimensions
  • B: Derivation of the Maxwell stress tensor
  • C: Time-derivative, divergence and curl of the fields of a monochromatic EM plane wave
  • D: EM field of a rectangular cross-section waveguide
  • E: Summary of vector calculus identities
  • Index

Raymond John Protheroe

Raymond Protheroe obtained his PhD in 1978 from Durham University, U.K., for a thesis on simulation of showers of energetic sub-atomic particles in the atmosphere produced by high energy cosmic rays (the highest energy particles in nature). He then spent the next three years in the U.S. as a NAS/NRC Fellow at NASA's Goddard Space Flight Center where he worked on the propagation and origin of cosmic rays. In 1983 Protheroe moved to the University of Adelaide in Australia on a Queen Elizabeth II Fellowship to work on cosmic rays and ground-based gamma-ray astronomy, and was appointed Associate Professor/Reader in 1998. He was elected Fellow of the RAS (1979), IoP (1984), AIP (1990), ASA (1996), and has been Vice-Chair of Commission C4 (Cosmic Rays) of the IUPAP (2002-2005) and a member of the IAU since 1986.

As an educator, Professor Protheroe has taught introductory physics, undergraduate courses in optics, electromagnetism, quantum mechanics, astrophysics and relativity and cosmology, and at honours (graduate level) classical electrodynamics and high energy astrophysics. An example of his commitment to fully understanding and explaining the physics being taught led to his writing a paper on a fundamental aspect of electromagnetism which was inconsistent between textbooks at the time (“The Transient Magnetic Field Outside an Infinite Solenoid” by R. J. Protheroe and D. Koks, 1996, American J. Physics, 64, 1389).

Dr Protheroe's research has ranged widely from topics such as cosmic ray acceleration, energetic particle interactions in terrestrial, astrophysical and cosmological environments to predicting fluxes of cosmic rays, radio to gamma-ray emission and/or neutrinos from pulsars, supernovae, supernova remnants, our Milky Way galaxy and active galactic nuclei. Together with radio-astronomer colleagues, he recently instigated projects using radio telescopes to do neutrino astronomy with large radio telescopes and the Moon as the neutrino target. Protheroe has given numerous invited talks at international conferences, been awarded prizes including the inaugural international Shakti P. Duggal Prize at the 19th International Cosmic Ray Conference held in La Jolla. Protheroe's research has led to well over 300 publications including more than 140 articles on his research in peer-reviewed scientific journals. Lists of his publications can be found at:

Dr Protheroe's publications on SAO/NASA Astrophysics Data System

Dr Protheroe's publications on INSPIRE