Course: PHY 6347, Electromagnetic Theory 2, Meeting times: MWF, Period 6 (12:50–1:40pm), room 1101
Instructor: J. N. Fry, Office: 2172, Phone: 392-6692, e-mail: fry # phys.ufl.edu, Office Hours: MWF, 10:00–12:00   [schedule]
Grader: Gaoli Chen, Office: 2060, Phone: 392-7003, e-mail: gchen # ufl.edu, Office Hours: M 3:00–5:00

Dmitrii's 6347 page Dmitrii's 6346 page

Course Description: PHY 6347 is the second semester of the graduate core sequence in Electromagnetism (the first half was PHY 6346), exploring implications of Maxwell's equations in general and in specific situations. The objectives of the course are (i) to study electrodynamics at a theoretically sophisticated level; (ii) to develop mathematical techniques useful for solving problems in E&M as well as other areas of physics; (iii) to develop problem solving skills; (iv) to prepare the student (if necessary) for the preliminary exam. In this semester we will develop applications of general principles introduced in the fall. Topics to be covered include

• time-dependent Maxwell equations, Green's function for wave equation
• conservation laws, energy density, energy flux (Poynting vector), momentum density, momentum flux (Maxwell stress tensor)
  harmonically varying fields, time average, tensors, duality
• Plane waves, propagation and dispersion; magnetohydrodynamics; Eikonal formulation for continuous media
• Confined geometries: waveguides, cavities, dielectric waveguides/fibers, losses and attenuation  [we have to leave out something]
• Radiation from harmonic sources: dipole and higher multipoles, linear antenna, vector spherical harmonic expansion
• Scattering and diffraction: Kirchhoff approximation, full partial wave expansion, short wavelength limit
• Special relativity: Lorentz transformations, spacetime vectors and tensors, proper time, 4-vector velocity, acceleration, energy-momentum,
  classical field theory, covariant formulation of electromagnetism
• Radiation from accelerated charges; synchrotron radiation, bremsstrahlung
• Collisions, energy loss in matter, multiple scattering  [again, probably not]
• non-Abelian theories  [if time allows]

Grading: Grading will be based 50% on periodic homework sets, and 25% each on a midterm and final exam. The midterm exam will be Monday February 26. [Solution] [Distribution] [average=90 ± 21]. The final exam is officially scheduled for Thursday May 3, 7:30–9:30am (Exam Group 3A). [Or 10:00.] [Solution] [Distribution] [average=71 ± 24]. Exams will be open textbook, but not open notes. Students are expected to complete work at the time due, or as soon as possible in case of illness or other accepted, documented circumstance. There will be no last-minute makeups accepted.

The following paragraphs of advice on how to do well in Physics are lifted from one of my colleagues. (He also was once known to have his posted office hours during class time.) This is a graduate course, and you are free to make your own choices, but you should listen to what they say:
  I do not plan to take daily attendance, but it is to your advantage to attend class. You may spend most of your time sleeping, but in between you will have the opportunity to learn what subjects I think are important, and you can then concentrate on these subjects during your reading. If by some unfortunate set of circumstances you do miss class, do not ask me if I said anything important — everything that I say is important. Instead, ask a classmate; she or he is likely to give an honest answer, and you won't offend me. There will be a substantial number of examples discussed in class that are not in the textbook, and examples in class often appear on tests. If you miss class you will not do well in this course.
  Do the assigned homework. This is the drudge part of physics, but it is absolutely necessary. We will learn grand ideas and see their wondrous applications in class. But, your understanding is only superficial unless you can apply these same grand ideas to completely new circumstances. In course work, this is usually done with homework problems. Do not be surprised if the homework is frustrating at times; solving one challenging problem makes the next much easier. And homework problems often appear on tests. Doing all of the homework is the easiest way to improve your grade. Not doing homework is the easiest way to lower your grade.

Required text:

• John David Jackson [ucb] [lbl] [cv] [aip px] [science.ca] Classical Electrodynamics, 3rd Edition (Wiley, 1999)   [errata] .
  Remembering J. D. Jackson, 1925–2016   In Memoriam: John David Jackson   John David Jackson (1925-2016)
  ΜΑΘΕΙΝ ΠΑΘΕΙΝ: A thesaurus of the idolect of John David Jackson

Other books:

• Andrew Zangwill, Modern Electrodynamics (Cambridge, 2013). [frontmatter] [errata]
• David J. Griffiths, Introduction to Electromagnetics, 4/E (Pearson Prentice Hall, 2013). author page includes errata links
• 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). ,
• Mark A. Heald and Jerry B. Marion, Classical Electromagnetic Radiation, 3rd edition (Dover reprint of Saunders, 1995).  
  (J. B. Marion, 1st ed, Academic Press, 1965). ^[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]

• Edwin F. Taylor and John Archibald Wheeler, Spacetime Physics, 2ed (W H Freeman, 1992)

• George Arfken, Mathematical Methods for Physicists, Third Edition (Academic Press, 1985).
• Philip M. Morse and Herman Feshbach, Methods of Theoretical Physics, Parts I, II (McGraw-Hill, 1953).
• 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

Kevin Schmidt's Possibly Useful Books for Classical Electromagnetism, with comments

The following quote (attributed to Sidney Coleman) captures a common reaction to Jackson: Scientists tend to overcompress, to make their arguments difficult to follow by leaving out too many steps. They do this because they have a hard time writing and they would like to get it over with as soon as possible.... Six weeks of work are subsumed into the word "obviously."

This and that:
Physical Constants from the Particle Data Group
Math trivia, Akira Hirose Math Notes, DLMF Bessel functions, more on Bessel functions
Integral of Bessel function multiplied with sine
Searches for magnetic monopoles
radio spectrum frequency allocations, 2011, 2016, fcc table (2015)
Wave Packet Animations (from A. John Mallinckrodt)
Model ε(ω), osa fig, DBT, PRB28 1983 [eq.(10), p.12].
Polarizations: ε(α|β), ε(β|α)   Poincaré sphere, Poincaré sphere Poincaré sphere
polarized reflection Hannes Alfvén
GR Quadrupole Formula
Rotating systems
Half-wave, full-wave antenna patterns, scaled. integrated power, P(kd), kd = 7 kd = 127
Spherical Bessel functions Scaling l j_l(x/l), and another scaling [l j_l(x/l)]^1/l
Vector spherical harmonic angular distributions
Linear Antenna: Multipole Expansion, (Δθ)² vs. kd narrow patterns
Conducting sphere: long wavelength dσ/dΩ for ka = 1/8, 1/4, 1/2, 1; Π, dσ/dΩ for polarizations
  short wavelength dσ/dΩ for ka = 1/2, 1, 4, 16, 64; scaled short wavelength; log dσ/dΩ vs. θ;
  amplitudes |α_l|², |β_l|² for ka=1, ka=64; integrated scattering cross section σ(ka). Short wavelength ka=128
Cross section σ(ka) for dielectric sphere with n = 4/3
Circular Aperture Diffraction, and again, Poisson's bright spot, square diffraction
Lorentz generators
twin paradox
Constant Acceleration
Lamborghini Adventador 2016, Centenario 2017, Sesto Elemento 2017 [(88 ft/sec) / (2.7 sec) = 32.6 ft/sec², (88 ft/sec) / (2.4 sec) = 36.6 ft/sec²]
spacetime trajectories
Lorentz boosted Coulomb electric field γ = 1, 1.020, 1.091, 5/4, 5/3, 10 (v/c = 0, 1/5, 2/5, 3/5, 4/5, 0.99499),   γ = √(3/2)
Alfred-Marie Liénard, Emil Johann Wiechert EJW
Field of displaced charge
Kevin Schmidt's 3+1 derivation of the relativistic Larmor formula
LHC Synchrotron radiation
large-γ f(θ), Lorentz transformed angular distributions
Emmy Nöther, Invariant Variation Problems, Nöther's [1918] Theorem. Thank you emmy Nöther

J. Clerk Maxwell, FRS, A Dynamical Theory of the Electromagnetic Field, Phil. Trans. R. Soc. Lond. 155, 459 (1865).
Contributions of John Henry Poynting to the understanding of radiation pressure, Proc. Royal Soc. Lond. A (2012).
J. H. Poynting, A COMPARISON of the FLUCTUATIONS in the PRICE of WHEAT and in the COTTON and SILK IMPORTS into GREAT BRITAIN, Journal of the Royal Statistical Society 47, 33–64 (1884)
P. A. M. Dirac, Quantised Singularities in the Electromagnetic Field, Proc. R. Soc. Lond. A 133, 60 (1931).
P. A. M. Dirac, The Theory of Magnetic Poles, Phys. Rev. 74, 817 (1948).
A. S. Goldhaber, Role of Spin in the Monopole Problem, Phys. Rev. 140, 1407 (1965).
H. A. Wilson, Note on Dirac's Theory of Magnetic Poles, Phys. Rev. 75, 309 (1949).
J. J. Thompson, ELEMENTS OF THE MATHEMATICAL THEORY OF ELECTRICITY AND MAGNETISM (1909), see Section 284, p. 532.
C. J. Bouwcamp, H. B. G. Casimir, On multipole expansions in the theory of electromagnetic radiation, Physica 20, 549 (1954).

And the other:
Hitler v Jackson, Hitler v spherical Bessel functions
Let it Snow
Collider, Mr Higgs Twist, Les Horribles Cernettes WiX site
LHC Street View
Bohemian Gravity, Entropic Time, Eminemium , William Rowan Hamilton
USB Wine
Skeetobite Weather, SFWMD computer tracks, HWRF
Tom Leherer has turned 90! The Elements, New Math, Lobachevsky, Wernher Von Braun, We Will All Go Together When We Go

Class Diary

Homework: Problem solving is a skill learned only through practice. Take advantage of the homework as an opportunity to learn how to recognize the right approach to a problem before it becomes exam time. While I encourage you to discuss the assignments with each other, what you turn in must represent your own work. As we also do when publishing research articles: if you obtain significant information from a published or human source, cite that source. This will often be as little as "Jackson, eq. (9.98)". If you work together, please identify other members of your working group. This edition of the textbook uses SI (mks) units, at least until the chapters on relativity. Correct solutions to the assigned problems will be in appropriate units. Best answers are reduced to simplest terms; ½ tan⁻¹[2az/(a²−z²)] is and is not the same as tan⁻¹(z/a) .

1. Homework 1, due Friday January 19. Solution
2. Homework 2, due Friday January 26. Solution
   The given t-dependence does not imply that the current does or does not have a z-dependence.
3. Homework 3, due Friday February 2. Solution
   cf. Fast Radio Burst Discovered in the Arecibo Pulsar ALFA Survey, L. G. Spitler et al., Ap. J. 790, 101 (2014)
   The Repeating Fast Radio Burst FRB 121102: Multi-wavelength Observations and Additional Bursts, P. Scholz et al., Ap. J. 833, 177 (2016)
   FRB 121102 casts new light on the photon mass, L.Bonetti et al., Phys Lett B 757, 548 (2016)
4. Homework 4, due Friday February 9. Solution
5. Homework 5, due Friday February 16. Solution
6. Homework 6, due Friday February 23. Solution
7. Homework 7, due Friday March 16. Solution
8. Homework 8, due Friday March 23. Solution
9. Homework 9, due Friday March 30. Solution
10. Homework 10, due Friday April 6. Solution
11. Homework 11, due Friday April 20. Solution

    Midterm Exam Solution
    Final Exam Solution

University Policies: Students are expected to know and comply with the University's policies regarding academic honesty and use of copyrighted materials. Cheating, plagiarism, or other violations of the Academic Honesty Guidelines will not be tolerated and will be pursued through the University's adjudication procedures.
  “Students requesting classroom accommodations must first register with the Disabilities Resources Program, located in the Dean of Students Office, P202 Peabody Hall. The Disabilities Resources Program will provide documentation to the student, who must then deliver this documentation to the instructor when requesting accommodations.”