Preface

Classical Electrodynamics is one of the most beautiful things in the world. Four simple vector equations (or one tensor equation and an asssociated dual) describe the unified electromagnetic field and more or less directly imply the theory of relativity. The discovery and proof that light is an electromagnetic wave stands to this day as one of the greatest moments in the history of science.

These four equations even contain within them the seeds of their own
destruction as a classical theory. Once Maxwell's equations were known,
the *inconsistency* of the classical physics one could then easily
derive from them with countless experimental results associated with
electromagnetism forced the classicists of the day, many of them
metaphorically kicking or screaming, to invent *quantum* mechanics
and *quantum* electrodynamics to explain them. Indeed, once the
single fact that an accelerated charged particle necessarily radiates
electromagnetic energy was known, it became virtually impossible to
conceptually explain the persistence of structure at the microscopic
level (since the forces associated with binding objects together out of
discrete charged parts inevitably produce an oscillation of charge due
to small perturbations of position, with an associated acceleration).,
The few hypotheses that were advanced to account for it ``without'' an
overtly oscillatory model were rapidly and decisively shot down by (now
famous) experiments by Rutherford, Millikan, and others.

Even though the Universe proves to be quantum mechanical at the
microscopic level, classical electrodynamics is nevertheless extremely
relevant and useful in the real world today at the *macroscopic*
level. It describes extremely precisely nearly all the mundane aspects
of ordinary electrical engineering and electromagnetic radiation from
the static limit through optical frequencies. Even at the molecular
level or photonic level where it breaks down and a quantum theory must
be used it is *first* necessary to *understand* the classical
theory before exploring the quantum theory, as the quantum theory is
built on top of the entire relativistic electrodynamic conceptual
framework already established.

This set of lecture notes is designed to be used to teach graduate students (and possibly advanced and motivated undergraduates) classical electrodynamics. In particular, it supports the second (more difficult) semester of a two semester course in electrodynamics that covers pretty much ``all'' of the theory itself (omitting, of course, many topics or specific areas where it can be applied) out to the points where the theory itself breaks down as noted above. At that point, to make further progress a student needs to learn about more fields, quantum (field) theory, advanced (general) relativity - topics generally beyond the scope of these notes.

The requirements for this course include a thorough understanding of electricity and magnetism at the level of at least one, ideally two, undergraduate courses. At Duke, for example, physics majors are first exposed first to an introductory course that covers the integral formulation of Maxwell's equations and light that uses no multivariate differential calculus, then a second course that develops the vector differential formulation of Maxwell's equations and their consequences) as does this course) but with considerably less mathematical rigor and completeness of the treatment as students taking it have likely still not had a course in e.g. contour integration. Students using these notes will find it useful to be at least somewhat comfortable with vector differential and integral calculus, to have had exposure to the theory and solution methodology of ordinary and partial differential equations, to be familiar with the mathematics of complex variables and analytic functions, contour integration, and it would be simply lovely if they at least knew what a ``tensor'' was.

However, even more so than is the case for most physics texts, this book
will endeavor to provide internal support for students that are weak in
one or more of these required mathematical skills. This support will
come in one of several forms. At the very least, considerable effort
has been made to hunt down on behalf of the student and explicitly
recommend useful textbooks and online resources on various mathematical
and physical topics that may be of use to them. Many of these resources
are freely available on the web. Some mathematical methods are
completely developed in the context of the discussion, either because it
makes sense to do so or because there simply *are* no references a
student is likely to be able to find. Finally, selected topics will be
covered in e.g. appendices or as insertions in the text where they are
short enough to be coverable in this way and important enough that
students are likely to be highly confused without this sort of support.

A very brief review of the *electrodynamics* topics covered
includes: plane waves, dispersion, penetration of waves at a boundary
(skin depth), wave guides and cavities and the various (TE, TM, TEM)
modes associated with them, radiation in the more general case beginning
with sources. This latter exhibition goes considerably beyond Jackson,
treating multipolar radiation in detail. It includes a fairly thorough
exposition of the underlying PDEs, the properties of the Green's
functions used to generate multipoles both approximate and exact, and
formally precise solutions that extend *inside* the source
charge-current density (as indeed they must for this formalism to be of
use in e.g. self-consistent field theories treating extended charge
density distributions). In addition to the vector spherical harmonics,
it defines and derives the properties of the Hansen multipoles (which
are otherwise very nearly a lost art) demonstrating their practical
utility with example problems involving antennae. It concludes this
part of the exposition with a short description of optical scattering as
waves interact with ``media'', e.g. small spheres intended to model
atoms or molecules.

It then procedes to develop relativity theory, first reviewing the
elementary theory presumably already familiar to students, then
developing the full Lorentz Group. As students tend to *not* be
familiar with tensors, the notes contain a special appendix on tensors
and tensor notation as a supplement. It also contains a bit of
supplemental support on at least those aspects of contour integration
relevant to the course for similar reasons. With relativity in hand,
relativistic electrodynamics is developed, including the properties of
radiation emitted from a point charge as it is accelerated. Finally,
the notes conclude with a nice overview of radiation reaction (exploring
the work of Lorentz, Dirac, and Wheeler and Feynman) and the puzzles
therein - self-interaction versus action at a distance, the need for a
*classical* renormalization in a theory based on self-interaction,
and a bit more.

One *note-worthy* feature of these notes (sorry, but I do like puns
and you'll just have to get used to them:-) is that the
electronic/online version of them includes several inventions of my own
such as a *wikinote*^{1} , a reference to supporting wikipedia articles that
appears as a URL and footnote in the text copy but which is an *active link* in a PDF or HTML (online) copy. Similarly, there are
google links and ordinary web links presented in the same way.

As noted at the beginning of the text, these are *real* lecture
notes and subject to change as they are used, semester by semester. In
some cases the changes are quite important, for example when a kind
reader gently points out a bone-headed mistake that makes some aspect of
the presentation quite incorrect. In others they are smaller
improvements: a new link, a slightly improved discussion, fixing clumsy
language, a new figure (or putting in one of the missing old ones). As
time passes I hope to add a selection of problems that will make the
text more of a stand-alone teaching aid as well.

For both of these reasons, students who are using these notes may wish
to have *both* a paper snapshot of the notes - that will *inevitably* contain omissions and mistakes or material I don't actually
cover in *this* year's class - *and* a (more current)
electronic copy. I generally maintain the current snapshot of the
electronic copy that I'm actually using to teach from where it is
available, for free to all comers, on my personal/class website at:

http://www.phy.duke.edu/rgb/Class/phy319.php

(which cleverly and self-consistently demonstrates an active link in action, as did the wikilink above). In this way they can have the convenience of a slightly-out-of-date paper copy to browse or study or follow and mark up during lecture as well as an electronic copy that is up to date and which contains useful active links.

Let it be noted that I'm as greedy and needy as the next human, and can
always use extra money. As I've worked quite hard on these notes (and
from observation they go quite beyond what e.g. most of my colleagues
make available for their own courses) I have done the work required to
transform them into an actual bound book that students *can* elect
to purchase all at once instead of downloading the free PDF, printing it
out as two-sided pages, punching it, and inserting it into a three ring
binder that anonymously joins the rest of their notes and ultimately is
thrown away or lost.

This printed book is remarkably inexpensive by the standards of modern
textbooks (where e.g Wyld, which I once purchased now at $16 a copy, is
not available new for *$70* a copy). At the same site, students
can find the actual PDF from which the book is generated available for a
very low cost and are at liberty to purchase and keep that on their
personal laptops or PDF-capable e-book readers, or for that matter to
have *it* printed and bound by a local printer. In both cases I
make a small royalty (on the order of $5) from their sale, which is both
fair and helps support me so that I can write more texts such as this.

However, students around the world have very different means.
Purchasing a $7.50 download in the United States means (for *most*
students) that a student has to give up a few Latte Enormes from
Starbucks. Purchasing that same download could be a real hardship for
students from many countries around the world *including* some from
the United States. For this reason students will always have the *option* of using the online notes directly from the class website for
free or printing their own copy on paper at cost. All that I ask of
students who elect to use them for free is that they ``pay it forward''
- that one day *they* help others who are less fortunate in some
way for free so that we can all keep the world moving along in a
positive direction.

These notes begin with *my* course syllabus and class rules and so
on. Obviously if you are reading this and are not *in* my class
these may be of no use to you. On the other hand, if you are a teacher
planning to use these notes to guide a similar course (in which case you
should probably contact me to get a free copy of the latex sources so
you can modify them according to your own needs) or just a student
seeking to learn how to most effectively *use* the notes and learn
electrodynamics effectively, you might still find the syllabus and class
rules worth at least a peek.

The one restriction I have, and I think it is entirely fair, is that
instructors who elect to use these notes to help support the teaching of
their own classes (either building them with or without modifications
from the sources or using any of the free prebuilt images) may not *resell* these notes to their own students for a profit (recovering
printing costs is OK) at least without arranging to send a fair share of
that profit back to me, nor may they alter this preface, the authorship
or copyright notice (basically all the front-matter) or the license.
Everything from the syllabus on is fair game, though, and the notes
should easily build on any e.g. linux system.

Anyway, good luck and remember that I *do* cherish feedback of all
sorts, corrections, additions (especially in ready-to-build latex with
EPS figures:-), suggestions, criticisms, and or course money in the form
of the aforementioned small royalties.