James Babington - Basic Electromagnetic Theory

B ASIC E LECTROMAGNETIC T HEORY

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B ASIC E LECTROMAGNETIC T HEORY

Field Theory Foundations and Structure

JAMES BABINGTON

MERCURY LEARNING AND INFORMATION

Dulles, Virginia

Boston, Massachusetts

New Delhi

Reprint and Revision Copyright 2017 by MERCURY LEARNING AND INFORMATION LLC. All rights reserved.

Original title and copyright: Basic Electromagnetic Theory: Field Theory Foundations and Structure. Copyright 2013 by James Babington. All rights reserved. Published by The Pantaneto Press.

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James Babington. Basic Electromagnetic Theory.

ISBN: 978-1-942270-74-4

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This book is intended as a short introduction to the foundations of electromagnetic field theory. It has been based on my experience both as a former field theorist (working on quantum field theories, quantum electrodynamics and Casimir physics) and currently as an applied optical physicist. Indeed, my thoughts were in the last couple of years to simply write down what I thought I knew and try to critically examine this. What has been very interesting to see is that, in my opinion, an appreciation of its history together with the characters involved is a necessity to get to grips with the foundations of the subject, and therefore understanding at a deeper level.

I was fortunate enough as an undergraduate to be exposed to some quite advanced electromagnetic field theory early on. My then tutor, Robin Devenish, at Hertford College, Oxford, set me some very interesting problems on electromagnetic fields written in the four-vector notation of special relativity at the end of my first year. This was real classical field theory that one would typically study before moving on to quantum fields. It came about because I actually wanted to study the general theory of relativity, and I had asked him how to get into it. In hindsight, these were exactly the right problems to work on over a summer vacation, and I thank him greatly for his direction here.

My prejudice is clearly going to be skewed towards the field theory aspects. However, and importantly, I have not shied away from experimental and measurement issues that ultimately are the reason for introducing a field theory in the first place. In particular, the historical demonstration of a principle, or the quantification of a law takes first place. The mathematics should be there to capture the essence of any experimental studies and provide a language with which to ask further questions. With this in mind, I am assuming on the part of the reader a genuine interest in the subject and present the material from this standpoint.

I have included some problems at the end with solutions; these are meant to illuminate parts of the text with either a definite calculation method, or to just see some numbers. In addition to these, exercises are scattered throughout the text to give a little poke to the reader to interact.

Finally, I would like to dedicate this book to my wife Serena and my son Albert with the very greatest affection.

James Babington

June 2016

Electromagnetism is perhaps the most basic theory we see around us in the natural world. It is responsible for the color we see, the forces that bind us together and for any technology beyond the steam engine. It is the theory par excellence in that it is responsible for the macroscopic world around us that we are part of and interact with. But it goes far beyond this as it is also the gateway to the sub-atomic world that tries to ultimately explain the existence of matter and forces. From these concepts must emerge the structures such as the atomic nuclei that are necessary to get any form of life going. Modern particle physics theories that try to explain the nature of quarks and the very small, and the evolution and dynamics of the universe on the other, take as their starting point something that looks quite similar to electromagnetism (that is the central role of gauge theories and symmetry as a governing principle).