Introduction to Electrodynamics, 4th Edition

Book Preface

This is a textbook on electricity and magnetism, designed for an undergraduate course at the junior or senior level. It can be covered comfortably in two semesters, maybe even with room to spare for special topics (AC circuits, numerical methods, plasma physics, transmission lines, antenna theory, etc.) A one-semester course could reasonably stop after Chapter 7. Unlike quantum mechanics or thermal physics (for example), there is a fairly general consensus with respect to the teaching of electrodynamics; the subjects to be included, and even their order of presentation, are not particularly controversial, and textbooks differ mainly in style and tone. My approach is perhaps less formal than most; I think this makes difficult ideas more interesting and accessible.
For this new edition I have made a large number of small changes, in the interests of clarity and grace. In a few places I have corrected serious errors. I have added some problems and examples (and removed a few that were not effective).

And I have included more references to the accessible literature (particularly the American Journal of Physics). I realize, of course, that most readers will not have the time or inclination to consult these resources, but I think it is worthwhile anyway, if only to emphasize that electrodynamics, notwithstanding its venerable age, is very much alive, and intriguing new discoveries are being made all the time. I hope that occasionally a problem will pique your curiosity, and you will be inspired to look up the reference—some of them are real gems. I have maintained three items of unorthodox notation:
• The Cartesian unit vectors are written xˆ, yˆ, and zˆ (and, in general, all unit vectors inherit the letter of the corresponding coordinate).
• The distance from the z axis in cylindrical coordinates is designated by s, to avoid confusion with r (the distance from the origin, and the radial coordinate in spherical coordinates).
• The script letterr denotes the vector from a source point r to the field point r (see Figure). Some authors prefer the more explicit (r − r ). But this makes many equations distractingly cumbersome, especially when the unit vector rˆ is involved. I realize that unwary readers are tempted to interpret r as r—it certainly makes the integrals easier! Please take note: r ≡ (r − r ), which is not the same as r. I think it’s good notation, but it does have to be handled with care.1

As in previous editions, I distinguish two kinds of problems. Some have a specific pedagogical purpose, and should be worked immediately after reading the section to which they pertain; these I have placed at the pertinent point within the chapter. (In a few cases the solution to a problem is used later in the text; these are indicated by a bullet (•) in the left margin.) Longer problems, or those of a more general nature, will be found at the end of each chapter. When I teach the subject, I assign some of these, and work a few of them in class. Unusually challenging problems are flagged by an exclamation point (!) in the margin. Many readers have asked that the answers to problems be provided at the back of the book; unfortunately, just as many are strenuously opposed. I have compromised, supplying answers when this seems particularly appropriate. A complete solution manual is available (to instructors) from the publisher; go to the Pearson web site to order a copy.
I have benefitted from the comments of many colleagues. I cannot list them all here, but I would like to thank the following people for especially useful contributions to this edition: Burton Brody (Bard), Catherine Crouch (Swarthmore), Joel Franklin (Reed), Ted Jacobson (Maryland), Don Koks (Adelaide), Charles Lane (Berry), Kirk McDonald2 (Princeton), Jim McTavish (Liverpool), Rich Saenz (Cal Poly), Darrel Schroeter (Reed), Herschel Snodgrass (Lewis and Clark), and Larry Tankersley (Naval Academy). Practically everything I know about electrodynamics—certainly about teaching electrodynamics—I owe to

Edward Purcell.
David J. Griffiths

Newtonian mechanics is adequate for most purposes in “everyday life,” but for objects moving at high speeds (near the speed of light) it is incorrect, and must be replaced by special relativity (introduced by Einstein in 1905); for objects that are extremely small (near the size of atoms) it fails for different reasons, and is superseded by quantum mechanics (developed by Bohr, Schrödinger, Heisenberg, and many others, in the 1920’s, mostly). For objects that are both very fast and very small (as is common in modern particle physics), a mechanics that combines relativity and quantum principles is in order; this relativistic quantum mechanics is known as quantum field theory—it was worked out in the thirties and forties, but even today it cannot claim to be a completely satisfactory system.

In this book, save for the last chapter, we shall work exclusively in the domain of classical mechanics, although electrodynamics extends with unique simplicity to the other three realms. (In fact, the theory is in most respects automat ically consistent with special relativity, for which it was, historically, the main stimulus.)

Four Kinds of Forces
Mechanics tells us how a system will behave when subjected to a given force.
There are just four basic forces known (presently) to physics: I list them in the
order of decreasing strength:

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1. Strong
2. Electromagnetic
3. Weak
4. Gravitational

The brevity of this list may surprise you. Where is friction? Where is the “normal” force that keeps you from falling through the floor? Where are the chemical forces that bind molecules together? Where is the force of impact between two colliding billiard balls? The answer is that all these forces are electromagnetic. Indeed, it is scarcely an exaggeration to say that we live in an electromagnetic world— virtually every force we experience in everyday life, with the exception of gravity, is electromagnetic in origin.

The strong forces, which hold protons and neutrons together in the atomic nucleus, have extremely short range, so we do not “feel” them, in spite of the fact that they are a hundred times more powerful than electrical forces. The weak forces, which account for certain kinds of radioactive decay, are also of short range, and they are far weaker than electromagnetic forces. As for gravity, it is so pitifully feeble (compared to all of the others) that it is only by virtue of huge mass con centrations (like the earth and the sun) that we ever notice it at all. The electrical repulsion between two electrons is 1042 times as large as their gravitational attraction, and if atoms were held together by gravitational (instead of electrical) forces, a single hydrogen atom would be much larger than the known universe.

Not only are electromagnetic forces overwhelmingly dominant in everyday life, they are also, at present, the only ones that are completely understood. There is, of course, a classical theory of gravity (Newton’s law of universal gravitation) and a relativistic one (Einstein’s general relativity), but no entirely satisfactory quantum mechanical theory of gravity has been constructed (though many people are working on it). At the present time there is a very successful (if cumbersome) theory for the weak interactions, and a strikingly attractive candidate (called chromodynamics) for the strong interactions.

All these theories draw their inspiration from electrodynamics; none can claim conclusive experimental verification at this stage. So electrodynamics, a beautifully complete and successful theory, has become a kind of paradigm for physicists: an ideal model that other theories emulate.

The laws of classical electrodynamics were discovered in bits and pieces by Franklin, Coulomb, Ampère, Faraday, and others, but the person who completed the job, and packaged it all in the compact and consistent form it has today, was James Clerk Maxwell. The theory is now about 150 years old