WAYNE SASLOW'S HOMEPAGE

Working manuscript by K. Rivkin and W. M. Saslow: Irreversible Thermodynamics of Non-Uniform Insulating Ferromagnets.

Course page for Physics 208, Summer of 2005.

Scientific Interests: Condensed Matter Theory: magnetism, semiconductors, electrochemistry, mixed ionic-electronic conductors, biophysics, superfluidity, superconductivity.

Teaching Interests: Electricity and Magnetism.  I am a former Associate Editor of the American Journal of Physics.  Three of my AJP papers have been listed as Most Memorable. References to various papers, or their results, are in at least six textbooks, including J. David Jackson's "Classical Electrodynamics" and David J. Griffiths "Introduction to Electrodynamics."  I am also a former Associate Editor for the Magnetism and Magnetic Materials Conference.

I have written ``Electricity, Magnetism, and Light (EM&L), '' published in 2002 by Harcourt/Academic-Elsevier. Originally conceived for Physics majors and honors students, I have also used it with non-honors classes. It is high on physics, but without an unnecessarily large amount of mathematics.  Michigan State's Gerald Pollock, co-author with Daniel Stump of the intermediate-level "Electromagnetism", has written me that all honors courses should be using EM&L.  In teaching intermediate E&M (TAMU Physics 304-305) I have found that student preparation is sufficiently weak that I must spend half of the first term reviewing introductory E&M (from EM&L), to ensure that students know how to use vectors, integral calculus, and vector calculus, on about 20 challenging first-year E&M problems.  Georgia Tech's Andrew Zangwill, author of "Physics at Surfaces", has written a very favorable post-use review.  EM&L has now been used for four consecutive terms, by four different faculty, at Georgia Tech.  It has also been used at Michigan State.  When my publisher provides me with the information, I will indicate the various schools at which it has been used. 

A set of worked-out Solutions to the odd-numbered problems is available from the publisher. 

Here are a list of text typos, a list of figure typos, and a corrected set of Answers to the odd-numbered problems.

A few of its unique points are:
1. A physically correct discussion of voltaic cells that is ``as simple as possible, but not any simpler''.
2. A practical approach to real magnets with application to the lifting strength of a refrigerator magnet.
3. A unified approach to the magnetism of currents wherein all of its laws are derived from the equivalence between magnets and current loops.
4. A general analysis of how a current-carrying wire moving in a static magnetic field can gain or lose kinetic energy without violating energy conservation.

Throughout the text, history is presented where conceptually relevant.  By relating experimental measurement and theoretical concepts, the text emphasizes the operational nature of physics.  Faculty interested in receiving an examination copy should email me their departmental mailing address.

Khondar Karim, Illinois State University: ``...the textbook by Saslow is exceptionally well-written. This book will stand out among many available textbooks on electromagnetism.  Its format is modern and user-friendly.  It emphasizes physical concepts, analyzes the electromagnetic aspects of many everyday phenomena, and guides the readers carefully through mathematical derivations.''  ``Apart from the prospect of being an excellent textbook for engineering students, this could serve as an excellent reference book for both physics and engineering students.''

Mike Sokoloff, U. Cincinatti: ``The text by Saslow is aimed at students taking a first substantial course in electricity and magnetism.  It carefully introduces all of the mathematical tools required to understand the physics content.  The emphasis on the relationship between equations (mathematics) and physics is very strong.'' ``The material covered is appropriate for a sophomore level course for physics and engineering students, probably a one semester course, although there is enough material for a two quarter course.  The style of writing is informal and invites the reader to stop and think about what has been said.  The illustrations anticipate students' questions and add to the clarity of the text's explanations.''

Carl Patton, Colorado State University: ``This text is a very good introduction to electricity and magnetism. There is a wealth of interesting and useful information, from the history of the science of electricity and magnetism, to connections with real world phenomena in science, engineering, and biology, to common sense advice and insight on the intuitive understanding of electical and magnetic phenomena, to take-home experiments to bring home the key concepts.''  ``This is a fun book to read, and I believe that students will find it `fun' too.''  ``The book is heavy on relevance.  Practical electrical examples, sections on motors and generators.'' ``The level is slightly more advanced than the standard freshman tests for calculus based engineering physics courses, but not much.''  ``The fare is pretty standard, but the delivery is exceptional.'' ``The approach is intuitive and pedagogical.  The focus is on using the mathematics (when needed) to better understand the physics, not just for the sake of doing the mathematics.''  ``Almost all of the mathematics is worked out clearly and concisely.  Clear and helpful diagrams accompany the mathematics at almost every stage.  The emphasis is always on intuitive physics, graphical visualization, and mathematical implementation.'' ``This text reads so easily and so well that I would probably overlook this style choice [too many we's] because of the excellent content and inherent interest the book consistently provokes.''  (Note: The  "we's" are gone.)

The chapter headings include quotations from Newton, Franklin, Ohm, Ampere, Faraday, Maxwell, Kelvin (aka W.Thomson), J.J.Thomson, Heaviside, Hertz, and Einstein.

As preparation for the writing process, I read Purcell. During the writing I read Maxwell (still full of gems), and toward the end I looked a bit at Feynman (whose book on E&M is much too sophisticated, both mathematically and physically, to be considered an introduction). The book avoids grad, and curl, but  emphasizes flux and circulation. As Maxwell points out (cf. the quotes at the beginning of Chapters 5 and 6), these are more in keeping with Faraday's way of looking at things.

Although the majority of the manuscript has a conventional structure, the first two chapters -- giving background and history -- do not. The harder material is clearly-marked as optional, and nearly always comes at the end of the chapter. Ten terms of students have debugged it . The first two chapters give a background in mathematics while building the experimental basis on which electrostatics was founded.

Chapter 0. Review and Preview of Electricity: Its Uses and Visualization (or: What You Should Have Been Taught in High School but Probably Weren't)provides an overview of electrostatics and electric current (but no magnetism), with a detailed and critical discussion of the electric fluid model. Here is the first figure -- a wall plug, where life begins:

This chapter presents a modern discussion of the properties of matter, in terms of electrons being in either localized orbitals (insulators) or extended orbitals (conductors). In particular, it discusses a physical picture of electric screening as a collective effect involving distorted electron orbitals. This chapter also discusses critically the electric fluid model, as well as Faraday's lines of force and how they relate to charge. The penultimate section is on energy flow in a wire. Last is a review of vectors, emphasizing the scalar product, the vector product, and the behavior of vectors under rotations.

Chapter 1. A History of Electricity and Magnetism, to Conservation of Charge provides a historical introduction to electrostatics, beginning with its discovery through the amber effect (e.g. a rubbed comb and a small piece of paper), and concluding with the formulation of the electric fluid model and a qualitative understanding of electrostatic induction. The Law of Charge Conservation is formulated with explicit, worked-out examples, often in the context of electrostatic induction. This is an attempt to get students to believe Charge Conservation is important, and it appears long before they have to use it to solve problems where capacitors must be connected. This is the first quantitative law of static electricity. Franklin, whose version of the electric fluid model led to the concept of charge conservation, also is responsible for another conservation law: ``A penny saved is a penny earned.'' The last section reviews integration and integrates over charge densities for some common geometries.

Chapter 2. Coulomb's Law for Static Electricity, Principle of Superposition continues the quantitative study of static electricity, with Coulomb's Law, which is discussed as an example of action-at-a-distance. Students are introduced to the idea that for every problem there are two figures: one that states the problem and one that the student generates in order to solve the problem.  A spreadsheet calculation of the force on a point charge due to a discretized uniformly-charged rod provides a check on the integral calculus solution to the same problem. The chapter ends with an optional discussion of the amber effect, showing that it is an inverse fifth power law. Chapters 2 and 3 provide the essential foundation for the next four chapters.

Chapter 3. The Electric Field Concept introduces the electric field idea, as a necessary consequence of the expected time-delay between an action and its distant effect. The idea of electric field-lines is developed, and field-line drawing is discussed in some detail. The amber effect is studied quantitatively, and the force on a polarized carbon atom due to the nonuniform field of a point charge is computed.

Chapter 4. Gauss's Law: Flux and Charge Are Related deals with Gauss's Law. The initial discussion begins with Faraday's idea of the proportionality of field lines to charge, and segues to a more quantitative expression in terms of electric flux. (Gauss's Law is a trial for both faculty and students; this discussion emphasizes physical ideas over compact mathematical formalism.) There is a particularly careful discussion of electrical screening, and how it is performed by charge rearrangement on the conductor. The text emphasizes the importance of being able to measure or calculate electric flux, which permits us to make a non-invasive determination of the charge enclosed by a given object. Symmetry calculations of the electric field are also given.

Chapter 5. Electrical Potential Energy and Electrical Potential. The concept of electric circulation is introduced, and shown to be zero for the electrostatic force acting over a closed path, from which the uniqueness of the voltage follows. Both the action-at-a-distance viewpoint, where the potential is the sum of the potentials due to many point charges, and the field viewpoint, where the potential is due to a line integral over the electric field, are considered in detail. The subtle but real patch effect, whereby the surface of a non-uniform conductor is not an equipotential, is discussed, and related to scanning tunnelling microscopy (STM). An anecdote, from Phil Platzman (ATT-Lucent), about Feynman's introduction to STM, is presented.

Chapter 6. Capacitance. Single-plate capacitors are discussed first, and what has been called Volta's Law: Q=C(DV) is introduced, both for one-plate and two-plate capacitors. (The symbol D will have to substitute for the Greek letter Delta.) We explain why, when the Leyden Jar was first discovered, many experimenters could not reproduce the results of the discoverers.  We show, in an optional section, that in recent superconducting tunnelling experiments the dependence on the presence of electric charge on yet other conductors is most naturally interpreted with the coefficients of potential.  The text emphasizes that problems involving capacitors involve only the Law of Charge Conservation and the uniqueness of the potential. The relationship between polarizability and dielectric constant, and the relationship between electron mean-free-path and the field for dielectric breakdown (relevant both to plasma globes and so-called plasma television), are discussed, and a careful discussion of electrical energy storage by capacitors is presented. In an optional section, Maxwell's coefficients of potential appear as an empirically determined set of numbers that permit us to treat the most general case of an arbitrary number of conductors, even those that do not have cancelling charges. This provides a natural explanation for recent superconducting tunnelling experiments which depend on the presence of electric charge on yet other conductors.  The chapter closes with an optional discussion of flux tube energy, tension, and pressure, following J.J.Thomson.

Chapter 7. Ohm's Law: Electric Current is Driven by EMF, and Limited by Electrical Resistance gives a serious but non-tehnical discussion of Ohm's Law and voltaic cells. This chapter was strongly influenced by Arnold Arons's remark that there is only one global version of Ohm's Law: I=DV/R. That is, a voltage difference drives current through a resistor, and thus a voltage difference can serve as an emf -- a point made by Maxwell. (To write this chapter required serious thought about what goes on inside batteries. This led to some legitimate research and a Physical Review Letter. I think no other physics text written in the past fifty years, without unnecessary complexity, gives as complete a discussion of this subject. Even Purcell and Feynman have difficulties discussing this material, although I prefer that in Purcell.) Here's the secret to understanding voltaic cells: the primary action in a voltaic cell is at the electrodes, where chemical reactions provide or remove energy, molecules, and electrons. Although interesting and complicated stuff goes on within the electrolyte, it is not too innacurate to describe the electrolyte as a resistance.  Thus a voltaic cell can be thought of as two surface pumps and a volume resistance.  There is a thorough discussion of emf, but space constraints forced me to remove a discussion of Faraday's Law of Electrolysis, and what it tells us about electricity and about conduction processes in electrolytes. See "Voltaic cells for physicists: Two surface pumps and an internal resistance," Wayne M. Saslow, Am. J. Phys. 67, 574 (1999).

Chapter 8. Batteries, Kirchoff's Laws, and Complex Circuits begins with some history of the voltaic cell. Neither Galvani nor Volta completely understood what he had done. Galvani thought the frog in his "metal A-metal B-frog-metal A" circuit was producing the electricity. Volta tried to ignore the chemical effects: he thought the driving energy was at the metal A-metal B interface, with the energy source being inexhaustible. Nevertheless, their results were significant because they were reproducible. The text next discusses batteries of voltaic cells, and the issues of efficiency (a number) and power transfer (watts). Next comes Kirchoff's Laws, done in three parts: Part 0 is the diagram defining positive directions of current flow for each arm; part 1 is charge (or current) conservation; part 2 is uniqueness of the voltage (part 2 uses the relation between voltage drop across a circuit element and its current or charge: either Volta's Law or Ohm's Law). The bridge circuit is done in detail, as an example of Maxwell's use of current loops. Only a two-by-two set of equations (for the two interior loop currents) need be solved to obtain the resistance of the bridge circuit in the general case. Ammeters and voltmeters are discussed in detail. The RC circuit is discussed in detail, and the differential equations are solved by numerical integration, by analytic integration, and by substitution of a trial solution with undetermined coefficients. Next comes the fact that charge distributed on the wire surfaces produces the electric field that drives current . The energy to set up the electric field can be written as (1/2)CV^2, and the resulting "parasitic capacitance," in parallel with the resistance, limits the short-time circuit response of the circuit. For fast IC's, designers avoid sharp corners, which require lots of charge, lots of field energy, and lots of parasitic capacitance. Hence, ninety degree turns on the electronic freeway are being replaced by two forty-five degree turns. The chapter closes with an optional discussion of plasma oscillations.  Interlude: Beyond Lumped Circuits (R's and C's). This discusses what has been done and what is to come. Some of the limitations of lumped circuits are discussed. It indicates the need for a theory that permits time delays; all the preceding material is, despite being couched in the language of fields, the same as for an action-at-a-distance theory.

Chapter 9. The Magnetism of Magnets follows J.J.Thomson, in that it uses the concept of magnetic charge. This makes it easy to perform the important practical calculation of how hard you have to pull to get a magnet off the refrigerator. As long as you are outside a magnet, you cannot tell that it does not contain magnetic charge that sums to zero. However, to counter the impression that magnetic charge exists, the deflection of muons when they pass through magnetized iron rings is discussed. They are deflected by the large magnetic B-field within the magnet (due to Amperian currents), not by the small magnetic H-field within the magnet. The analogy between electricity and the magnetism of magnetic charges means that students get to practice their electrostatics, in disguise. The various types of magnetism are briefly discussed, as are hysteresis loops and how they apply to tthe design of permanent magnets, hard drives, and electromagnets. Both compass-needle motion and nuclear magnetic resonance are treated.

Chapter 10. How Electric Currents Interact with Magnetic Fields considers the forces on current-carrying conductors and on moving charges. It begins by presenting Oersted's result and giving Oersted's right-hand-rule for the magnetic field due to a long current-carrying wire. It then goes on to present the important experimental equivalence-at-a-distance, due to Ampere (hence, Ampere's Wonderful Equivalence), between a magnet and a current loop of suitable magnetic moment. Ampere's right-hand-rule for the magnetic moment of a small current loop is then given. From this result, and the properties of magnets in a magnetic field, the force law for a current-carrying wire is deduced, and from that, the Lorentz force law is deduced. In archaic but accurate terminology, the first is called a ponderomotive force (since it acts on a macroscopic body), and the second is called an electromotive force (since it acts on the charges that produce electric currents).  The chapter concludes with an optional section showing that, although the magnetic force can do zero work, the ponderomotive force does do work, which is compensated by an equal amount of negative work done on the current by the electromotive force.  This argument, for a circuit as a whole, was likely known to Kelvin.

Chapter 11. How Electric Currents Produce Magnetic Fields: The Biot-Savart Law and Ampere's Law. These laws are derived from Ampere's Wonderful Equivalence. Lots of examples are worked out, and it is shown how the analogy between electricity and magnetism can enable us to use magnetism to get at the fringing field of a capacitor. Optional sections discuss perfect diamagnetism and the evidence that microscopic Amperian currents flow in ordinary magnets, whereas macroscopic currents flow in perfect diamagnets.

Chapter 12. Faraday's Law of Electromagnetic Induction begins with a historical introduction. It then gives a more detailed and systematic discussion of the electromechanical manifestations of Faraday's Law than I have seen elsewhere. Mutual and self-inductance are introduced together, thus giving a unified view of electromagnetic induction. A careful discussion of the experiment of young Mr.Jenkin, who told Faraday of the phenomenon that led to Faraday's discovery of self-induction, is used to motivate the discussion of the LR circuit. By careful use of Ohm's Law, it is deduced that the electrostatic voltage across an ideal (resistanceless) inductor is exactly opposite to the emf due to Faraday's Law. The chapter closes with a discussion of a three-arm circuit where a battery with a closed switch is in parallel with two real inductors (with resistance), and how current flows through the inductors just after the switch is opened.

Chapter 13. Mechanical Implications of Faraday's Law: Motors and Generators attempts to reclaim for physics some of the magic of motors and generators. Rather than relegating the principles of these interesting devices to homework problems, this chapter pulls these topics out of the shadows. To motivate the material, it recalls some history of this area, and how the efficiency of motors and generators went from no more that 35% in 1876 to over 80% by 1880. The answer was the discovery of eddy current heating in the inefficiently-designed machines. A later improvement of an additional 10% came from the use of magnetic materials with less hysteresis loss.

Chapter 14. Alternating Current Phenomena: Signals and Power treats ac circuits. First LC resonance is discussed, followed by a discussion of the effects of resistance on such a circuit. Then ac power is discussed, and its effect on each of R, L, and C. After applying the principles to filters and resonators, as well as discussing transformers with more care than typical, it also discusses Elihu Thomson's Jumping Rings, and the complex Tesla coil circuit. The chapter ends with an optional discussion of electromagnetic screening by a semi-infinite metal. It is shown that the voltage near a Tesla coil doesn't hurt you because you don't charge much at such high frequencies, not because the radiation doesn't penetrate you (it does!).

Chapter 15. Electromagnetic Radiation. Following a brief history  after reminding students of how much their lives depend upon cable, microwave, radio and television, Maxwell's new term -- the displacement current -- is introduced. Assuming that students are not familiar with the wave equation for a string, it is derived, and applied to the theory of guitar tuning (standing waves) and of propagating waves. (Waves of longitudinal compression are discussed in an optional section at the chapter end.)  With this as background, Maxwell's equations in integral form are employed to obtain the properties of plane electromagnetic waves. The Poytning vector is then reintroduced, and both energy and momentum flow are considered. A discussion of polarization is given, as well as the effect of a material medium on the velocity of light, and on the bending of light at an interface. Then the experiments of Hertz, using microwave radiation, are described.

Chapter 16. Physical Optics. After first discussing the history of the subject, including arguments for and against the wave viewpoint,  Thomas Young's work on interference is discussed in various contexts, from water waves to light waves and Newton's rings.    (Young really understood a great deal about temporal and spacial coherence.) Then  comes Fresnel and his Huyghens-based theory of diffraction.  The chapter closes with a discussion of diffraction gratings, and what can be learned about the stars from study of the light they emitted long, long ago.

In addition to the above chapters in "Electricity, Magnetism, and Light," the following material is available as a pdf file (just email me at wsaslow@tamu.edu):

Chapter 17. Image Formation and Optical Instruments. This chapter begins a discussion of flat mirrors and lenses, to establish sign conventions for the object and the image, and then goes on to study non-flat mirrors and lenses.  The eye, the camera, the microscope and telescopes are discussed, including considerations on the so-called circle of confusion that is relevant for determining depth-of-field.  Following an article in Optics News by the physics Charles Falco and the artist David Hockney (inspired by Hockney's book "Secret Knowledge"), we discuss he camera lucida used my early Renaissance artists.  The chapter ends with a demonstration that, for a concave mirror and an off-axis object (rather than an on-axis object, as normally discussed), all paraxial rays pass through the same point.

Speaking of light from long, long ago, here is a picture of my mom, taken in 1942, when she was 23.