# PHYS 3220 - Physics for Scientists II (Honors) - Fall 2017

## Supplements

### Useful stuff

A table of common SI prefixes, with pronunciation and probable origin.

The Gauss's Law Tabloid is a two-sheet summary with examples on how to use Gauss's Law for planar, cylindrical, and spherical symmetries.

Maxwell's equations and the Lorentz force law in components can be found here.

Here is page 232, which is missing from the 2014 printing of the textbook.

Although the derivation of the gradient, divergence, and curl formulas for general orthogonal curvilinear coordinates can be found in many books, I have found the following notes by James Foadi simple and clear: Gradient, divergence, and curl in curvilinear coordinates.

There are many books introducing the theory of special relativity. Appendix G in Purcell & Morin is quick summary of the important properties needed for this class. For further reading I suggest Robert Resnick, Introduction to Special Relativity (1968) or the freely-available notes by Robert Katz, An introduction to the Special Theory of Relativity (1964).

### PhET Interactive Simulations

The PhET interactive science simulations are a great way to enhance your understanding of electricity and magnetism (and other parts of science, too). They are based on educational research and can be great fun, even those aimed at middle school students. Since the PhET simulations are physically accurate, you are actively encouraged to spend time and “experience” them to enhance your understanding of electromagnetism.

Here are the links to notable simulations directly related to material covered in this course:

Other relevant simulations are found in the categories Electricity, Magnets, and Circuits and Light and Radiation on the PhET website.

(For Mac OS 10.8 and later users: you need Java to run the PhET simulations. If your browser does not run them, download the file and launch it by double-clicking and choosing Open.)

### Is magnetism a relativistic aspect of electricity?

Purcell and Morin's textbook states that magnetism is a relativistic aspect of electricity and that the magnetic force is a consequence of Coulomb's law, charge invariance, and relativity. Is it true? Should other assumptions be made? Or is it rather that electric and magnetic fields are two facets of a single object, the electromagnetic field? Consider the following thoughts.

Newton's law of gravitation is similar in form to Coulomb's law, and one could repeat the derivations in the textbook to eventually obtain a gravitomagnetic field (Heaviside, 1893, "A gravitational and electromagnetic analogy", The Electrician 31:81, as cited in Gravitoelectromagnetism). The resulting theory is however not in accord with special relativity and is not Einstein's General Relativity.

According to the relativistic electromagnetism page on Wikipedia, an effort to mount a full-fledged electromechanics on a relativistic basis is seen in the work of Leigh Page, from the project outline in 1912 (American Journal of Science 32:16) to his textbook "Electrodynamics" (Page and Adams, 1940). A revival of interest in this method for education and training of electrical and electronics engineers broke out in the 1960s after Richard Feynman’s textbook "The Feynman Lectures on Physics", volume 2. Author J.R. Tessman proclaimed "Maxwell — Out of Newton, Coulomb and Einstein" (American Journal of Physics 34:1048).

In a 1996 paper (Jefimenko.pdf), Oleg Jefimenko shows that electricity is a relativistic aspect of magnetism: if one assumes that the interaction between moving electric charges is entirely due to the magnetic field, then relativity imposes the existence of an electric field. Jefimenko concludes that the idea of a single force field, be it magnetic or electric, is incompatible with relativity.

Electrons and other elementary particles carry dipole magnetic fields, which have been measured. If the dipole magnetic moment μ of the electron were due to the rotation of a uniformly charged sphere of radius R, then its equatorial rotation velocity v=15μ/(4πeR) would be smaller than the speed of light only if the electron's radius were more than 200 times larger than the proton's radius, in contradiction with experiments.