Classical Electromagnetic Theory

Professor Thomas Curtright

PHY650, Section RF

T,Th 1:40-2:55 room 203; W 1:00-1:50 room 110

Grade = HW + Midterm (Thurs 16 Oct) + Final (Wednesday 10 Dec)

Final Exam 2:00-4:30 pm, Wednesday, 10 December, in the Physics Library.

Required text: John David Jackson, Classical Electrodynamics, Third Edition (Wiley, 1999) [Jackson errata]

We will cover Chapters 1 - 8, more or less.  Notes on Bessel functions.  Notes on vector potentials.

A colloquium on magnetism, including lots of history.  More history is here:  Maxwell and Riemann.

 HW#1, due 17 September:  In-class problem - If the potential is modified from Coulomb form, 1/r, to Yukawa form, e-r/L/r, find the charge q induced on a conducting sphere of radius R1 when placed inside a concentric conducting sphere of radius R2 > R1.  Suppose both spheres are initially uncharged, but connected by a conducting pathway (wire).  Then charge Q is placed uniformly on the external sphere.   Express q in terms of Q, R1, R2, and L.  You may assume L >> R2. Jackson 1.3, 1.4 (also determine potentials, and plot them), 1.5, 1.14, 1.21, 1.24 (first remove effects of charge density by solving exactly for a potential that satisfies Poisson's equation, and then adjust b.c. accordingly for resulting relaxation problem) HW#2, due 1 October: Jackson 2.3, 2.6, 2.7, 2.12, 2.17, 2.26 HW#3, due 8 October: Jackson 3.2, 3.7, 3.8, 3.26 HW#4, due 15 October: Jackson 3.17, 3.20, 4.7. HW#5, due 31 October: Jackson 4.5, 4.10, 4.13, 5.3, 5.8, 5.9. HW#6, due 14 November: Verify in detail Eq(5.37) for the current ring vector potential. Jackson 5.18, 5.23, 5.25. HW#7, due 26 November: Jackson 5.35, 6.6, 6.8, 6.11, 6.14. NW#8, due 9 December: Jackson 6.18, 6.24, 7.2, 7.7, 7.22.

I have posted solutions in the Physics Library to those problems underlined above.
There may exist better solutions to any given problem.  In particular, if you find ERRORS
in any of the posted solutions, it is part of your task as students to correct those errors
and bring the corrections to my attention.

However, you must list all references, collaborations, and other sources, if any, for your HW solutions.

The content of the course is given, in summary, by the Lorentz force law and Maxwell's equations.

where

where

An exact expression for the Coulomb constant is:

Maxwell's Equations

Maxwell's equations relate the field quantities, the charge density, and the current density at one single point in space, through their time and space derivatives. They contain physical information obtained from Coulomb's, Ampere's, and Faraday's laws, and they have been modified by Maxwell's assumption so as to satisfy the law of continuity of charge. Below are Maxwell's equations and related equations. Bold-face letters represent vectors.

The symbols used in the above equations have the following meaning.

 Symbol Meaning MKS units Gaussian units magnetic induction (tesla) (gauss) velocity of light (meters per second) (centimeters per second) electric displacement (newtons per coulomb) (dynes per statcoulomb) electric field strength (newtons per coulomb) (dynes per statcoulomb) force (newton) (dyne) magnetic field intensity (amperes per meter) (gauss) current density (amperes per square meter) (gauss per meter) magnetization (amperes per meter) (gauss) charge (coulomb) (statcoulomb) volume charge density (coulomb per cubic meter) (statcoulomb per cubic centimeter) velocity (meters per second) (centimeters per second)

Other useful books:

Asim Orhan Barut, Electrodynamics and Classical Theory of Fields and Particles (Macmillan, 1964; Dover, 1980).

Sandra C. Chapman, Core Electrodynamics (Taylor & Francis, 2000).

Richard P. Feynman, Robert Leighton, and Mathew Sands, The Feynman Lectures on Physics, Volume II (Addison-Wesley, 1964).

Mark A. Heald and Jerry B. Marion, Classical Electromagnetic Radiation, 3rd edition (Brooks Cole, 1994). [1]

L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Fourth Revised English Edition.

Course of Theoretical Physics Volume 2 (Pergamon, 1975, 1987, 1997). [1]

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2d edition.

Course of Theoretical Physics Volume 8 (Pergamon, 1960, 1984, 1993). [1]

Francis E. Low, Classical Field Theory (Wiley, 1997). [1]

W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism, 2nd edition (Addison-Wesley, 1962).

Edward Purcell, Electricity and Magnetism (McGraw-Hill, 1984). [1]

Julian Schwinger, Lester L. DeRaad, Jr., Kimball A. Milton, and Wu-yang Tsai, Classical Electrodynamics (Perseus, 1998). [1]

Davison Eugene Soper, Classical Field Theory (John Wiley & Sons, 1976). [2]

M Abramowitz and I E Stegun, Handbook of Mathematical Functions,  (National Bureau of Standards, AMS 55, 1964)

George Arfken, Mathematical Methods for Physicists, Third Edition (Academic Press, 1985).

W H Press, S A Teukolsky, W T Vetterling, and B P Flannery, Numerical Recipes, (Cambridge University Press, 1992).

Harry M. Schey, Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Third Edition (W.W. Norton, 1997).

[1] Gaussian units; [2] Lorentz units