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Spie Press Book

Maxwell's Equations of Electrodynamics: An Explanation
Author(s): David W. Ball
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Book Description

Maxwell's Equations of Electrodynamics: An Explanation is a concise discussion of Maxwell's four equations of electrodynamics-the fundamental theory of electricity, magnetism, and light. It guides readers step-by-step through the vector calculus and development of each equation. Pictures and diagrams illustrate what the equations mean in basic terms. The book not only provides a fundamental description of our universe but also explains how these equations predict the fact that light is better described as "electromagnetic radiation."

Book Details

Date Published: 19 November 2012
Pages: 104
ISBN: 9780819494528
Volume: PM232

Table of Contents
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1. History
1.1 History (Ancient)
1.2 History (More Recent)
1.3 Faraday

2. First Equation of Electrodynamics
2.1 Enter Stage Left: Maxwell
2.2 A Calculus Primer
2.3 More Advanced Stuff
2.4 A Better Way
2.5 Maxwell's First Equation

3. Second Equation of Electrodynamics
3.1 Introduction
3.2 Faraday's Lines of Force
3.3 Maxwell's Second Equation

4. Third Equation of Electrodynamics
4.1 Beginnings
4.2 Work in an Electrostatic Field
4.3 Introducing the Curl
4.4 Faraday's Law

5. Fourth Equation of Electrodynamics
5.1 Ampère's Law
5.2 Maxwell's Displacement Current
5.3 Conclusion

Afterword: Whence Light?
A.1 Recap: The Four Equations
A.2 Whence Light?
A.3 Concluding Remarks


As the contributing editor of "The Baseline" column in Spectroscopy magazine, I get a lot of leeway from my editor regarding the topics I cover in the column. For example, I once did a column on clocks, only to end with the fact that atomic clocks, currently our most accurate, are based on spectroscopy. But most of my topics are more obviously related to the title of the publication.

In late 2010 or so, I had an idea to do a column on Maxwell's equations of electrodynamics, since our understanding of light is based on them. It did not take much research to realize that a discussion of Maxwell's equations was more than a 2000-word column could handle—indeed, whole books are written on them! (Insert premonitional music here.) What I proceeded to do was write about them in seven sequential installments over an almost two-year series of issues of the magazine. I've seldom had so much fun with, or learned so much from, one of my ideas for a column.

Not long into writing it (and after getting a better understanding of how long the series would be), I thought that the columns might be collected together, revised as needed, and published as a book. There is personal precedent for this: In the early 2000s, SPIE Press published a collection of my Spectroscopy columns in a book titled The Basics of Spectroscopy, which is still in print. So I contacted then-acquisitions-editor at SPIE Press, Tim Lamkins, with the idea of a book on Maxwell's equations. He responded in less than two hours. . . with a contract. (Note to budding authors: that's a good sign.)

Writing took a little longer than expected, what with having to split columns and a year-long professional sojourn to Colorado, but here it is. I hope the readers enjoy it. If, by any chance, you can think of a better way to explain Maxwell's equations, let me know—the hope is that this will be one of the premiere explanations of Maxwell's equations available.

Thanks to Tim Lamkins of SPIE Press for showing such faith in my idea, and for all the help in the process; also to his colleagues, Dara Burrows and Scott McNeill, who did a great job of converting manuscript to book. Thanks to the editor of Spectroscopy, Laura Bush, for letting me venture on such a long series of columns on a single topic. My gratitude goes to the College of Sciences and Health Professions, Cleveland State University (CSU), for granting me a leave of absence so I could spend a year at the US Air Force Academy, where much of the first draft was written, as well as to the staff in the Department of Chemistry, CSU, for helping me manage certain unrelinquishable tasks while I was gone. Thanks to Bhimsen Shivamoggi and Yakov Soskind for reading over the manuscript and making some useful suggestions; any remaining errors are the responsibility of the author. Never-ending appreciation goes to my family—Gail, Stuart, and Casey—for supporting me in my professional activities. Finally, thanks to John Q. Buquoi of the US Air Force Academy, Department of Chemistry, for his enthusiastic support and encouragement throughout the writing process.

David W. Ball
November 2012

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