Changed final exam date.
Watch this space for changes.
PHYS 6210: Electrodynamics and Classical Field Theory (Dr. Harald W. Griesshammer) in combination with
PHYS 6230: Computational Physics II, Electrodynamics-segment (Dr. Harald W. Griesshammer)
Lectures: Tuesday, Thursday 12:20 to 14:00 in Staughton 103. All lectures are 100 minutes, equivalent to 4 credit hours.
"Snow Days" (if we need to reschedule lectures, these are possible slots): Thursday 17:00 to 18:40 in Staughton 103 or Wed 16:00 to 17:40 in Staughton 103.
Surgery hours:
Start Thursdays at 14:00 in
Staughton 103. Lasts
till all questions are answered.
Homework Due: Wednesdays at
16:00hrs. Zero points for assignments not turned in
on time, unless you notify me before the due date with reproducibly legitimate reasons (e.g.~illness).
Additional
office hours
by appointment after 3pm in my office. Email what and when to discuss.
email: hgrie
<at> gwu.edu
Audience
First-year graduate students.
Goals
Introduction into the theoretical concepts and mathematical methods of Classical Electrodynamics as example of a relativistic Field Theory. Focus on skill-building, symmetry principles, controlled approximations, and concepts at the fore-front of research.
An incomplete, over-achieving, informal list of Questions to Check Your Progress can be found here. Under no condition is this a survey of material for exams -- neither maximal nor minimal. It might not even be of any use at all.
Prerequisites
Undergraduate Electrodynamics on the level of Griffith: Introduction to Electrodynamics, Chaps. 1-6; advanced undergraduate mathematical methods; undergraduate Quantum Mechanics.
The graduate courses in Autumn, in particular PHYS 6110: Mathematica Methods of Theoretical Physics and the chapters on Lagrangean Mechanics and Relativity in PHYS 6120: Classical Mechanics, are indispensable. See the first two paragraphs in the Questions to Check Your Progress.
Co-requisite
PHYS 6230: Computational Physics II (Haberzettl/Griesshammer).
Coordinated with: PHYS 6220: Quantum Mechanics I (Haberzettl)
Exams and Grading
The final grade is a sum of:
- Exercises/Homework (20% of total): weekly;
- Mid-Term Exam (40% of total): Wednesday, 22 Mar 8:30 to 10:30 in Staughton 103, 2 hours;
- Final Exam (40% of total): Tuesday, 16 May 9:30 to 12:00 in Staughton 103, 2.5 hours.
separately. In particular, you need at least 50% of all points in all Problem sheets together (not per sheet!). An excellent score usually starts at 80% of all points. Exams are closed-book. A sheet with some possibly relevant mathematical formulae will be provided by me in the days before each exam.
Exercises/Homework
Problem sheets are online Wednesdays and posted on this web-site (see below), due the following Wednesday at 16:00am.Drop hardcopies in my pigeon-hole in the Physics office or fax to 994-3001, or mail to hgrie <at> gwu.edu . No grace period granted.
Graded solutions are returned and discussed during the next Surgery hour.
Handwritten solutions must be on 5x5 quadrille ruled paper; electronic solutions must be in .pdf format.
Use of a "lab-book'' or "journal'' for homework is strongly encouraged.
Contents (with links to manuscripts -- see Caveat/Warning/Disclaimer)
- Fundamental Equations of Electrodynamics (1 lecture)
- Electrodynamics as Relativistic Field Theory (3+1 lectures)
- Electrostatics (2 lectures)
- Magnetostatics (1 lectures)
- Radiation and Radiating Systems (7 lectures)
- Scattering Theory (2+1 lectures)
- Electrodynamics in Matter (9-1 lectures)
- Advanced Topics (time permitting)
Syllabus: More Information/Bibliography/Units/Conventions
The only authoritative version of the syllabus contains much more information and is available as as .pdf-file: edyn.information.pdfFurther files: Conventions used; Essential Math and Physics formulae and numbers (what one needs to know in one's sleep).
Bibliography
There is no required reading for this course. You will not be able to find all aspects of the lecture explained well in only one textbook. Moreover, it is an essential part of the learning process to view the same topic from different angles, i.e. using different textbooks. Here is a list of those which I found most useful. If you discover others, tell me.
The Class schedule lists for each lecture recommended readings.
An asterisk * indicates titles on Course Reserve at Gelman Library, with max. 3 days for loan. Be social.
Mathematical Supplements:
[M] G.B. Arfken and H.J. Weber: Mathematical Methods for Physicists; 4th edition, Academic Press, ca.~78$. Not necessarily the best choice...
On Theoretical Electrodynamics:
- [Brau] * Ch.A. Brau: Modern Problems in Classical Electrodynamics; Oxford University Press; ca. 98$. Modern treatment, closely follows course-schedule. List of errata at http://www.vanderbilt.edu/AnS/physics/brau/book/Errata.html.
- [Lan2] * L.D. Landau and E.M. Lifshitz: The Classical Theory of Fields [Course of Theoretical Physics Series, Vol. 2]; 4th ed., Butterworth-Heinemann; ca. 45$.
- [Lan8] * L.D. Landau, E.M. Lifshitz and L.P. Pitaevskii: Electrodynamics of Continuous Media [Course of Theoretical Physics Series, Vol.~8]; 2nd ed., Butterworth-Heinemann; ca. 45$.
- [Jack] * J.D. Jackson: Classical Electrodynamics; 3rd ed., John Wiley, ca. 100$. List of errata at http://www-theory.lbl.gov/jdj/Errata-%2702-%2708.pdf.
- [Grif] D.J. Griffith: Introduction to Electrodynamics; 3rd ed., Prentice Hall; ca. 102$.
- [Schwa] M. Schwartz: Principles of Electrodynamics; Dover; ca. 12$.
[Ein1] Link to annotated English translations Einstein's paper of the Annus Mirabilis 1905; another link with more background.
[Ein2] A. Einstein: Relativity: The Special and General Theory; Penguin Classics.
[Ein3] A. Einstein: The Principle of Relativity; Dover.
[Born] M. Born: Einstein's Theory of Relativity; Dover.
Lecture Manuscript
A scanned version of a chapter-by-chapter manuscript can be found by following the links of chapter headings in the Class Schedule and Contents Section. The files are in .djvu-format, which is at present the most condensed way of storing scanned images: 50 scanned pages translate into 1.2 Gbytes of bitmap, or 50 MBytes .pdf or 4.7 MBytes of .djvu. The freeware djvu reader "djvulibre" for all operating systems is available at http://djvu.sourceforge.net/, or as add-on to every decent Linux distribution.Caveat: Warning and Disclaimer
These are my notes for preparing the class, in my handwriting.While considerable effort has been invested to ensure the accuracy of the Physics presented, this script bears only witness of my limited understanding of the subject. I am most grateful to every reader who can point out typos, errors, omissions or misconceptions. Maybe over the years, with lots of student participation, this can grow into something remotely useful.
The script only intends to ease the pain of following the lecture, and does not replace the thorough study of textbooks.
The script is not intended to be comprehensible, comprehensive -- or even useful.
It is certainly not legible.
Your mileage will vary.
This script is not useful or relevant for exams of any kind.
Best Practice
Read over the manuscript before class. Try to grasp the essential points. The better prepared you are, the more we can focus on discussing your questions and observations, and solve problems. The class becomes more interactive and thus more fun -- and therefore you learn more.
Study details of the manuscript after the lecture, and follow the derivation of all formulae line-by-line. This is excellent and free exercise for your math skills, and makes sure you not just "read long". It is also the starting point for your own literature research using good books like those recommended for particular subjects in the "Suggested Reading" column below.
Class Schedule (no exact match, but an outline how we hope to progress)
Date | Topics (link to .djvu-file with manuscript) | Suggested Reading | Exercises |
. |
Revisit
your
undergraduate course notes. Revisit your Mathematical Methods course notes, in particular: partial differential equations, Dirac's δ-Distribution (handout), Green's functions, Fourier transforms (handout), spherical harmonics and multipole expansion (handout). Revisit your Theoretical Mechanics notes on Lagrangean Mechanics and on Special Relativity. |
See the first two paragraphs in the Questions to Check Your Progress. | 1.
Syllabus 2. Goals 3. Conventions 4. Math and Physics Essentials |
17 Jan, Tue lecture 1 moved to Mon 23 Jan 11:00-12:40 in Sta 208 (replaces QM-I) |
Syllabus
& Philosophy Fundamental Equations of Electrodynamics (1 lecture) recap: Interpretation of Maxwell's equations, Poisson equation, Gauss', Stokes' and Helmholtz' theorems, scalar and vector potentials, conventions Electrodynamics as Relativistic Field Theory (3+1 lectures) recap Special Relativity: postulates, Lorentz transformations, co- and contra-variant 4-vectors, |
[manu-script Fundamentals] Mathematical Methods lecture [Brau, chap. 0.1-5] [Jack, Intro] [M, chaps. 1&2, 3.3, 8.1, 8.7] (the latter cursorily) [Jack, chap. 6.10.A&B] [manu-script EDFT 1-4] Mechanics lecture [Brau, chap. 1.1-3, 2.1] [Lan2, chap. 1-9] [Jack, chap. 11.1-4,6-8] see also [Ein1, Ein2, Ein3, Born] |
Problem
sheet 1 special due 1 Feb, but you can do problems 1, 2, 4 and 6 without the first lecture! |
19 Jan, Thu lecture 2 moved to Wed 25 Jan 16:00 |
relativistic
mechanics of point
particles Link to nice visualisations of relativistically moving objects (look for "Film Index" and "First-Person Visualisations"; partially in German) particle in external 4-vector gauge field, electric and magnetic fields from the field strength tensor; |
[manu-script EDFT 5-20] see above |
|
24 Jan, Tue lecture 3 |
electric
and
magnetic fields from the
field
strength tensor (cont'd); Lorentz-transformation
of electric and magnetic fields, gauge freedom, gauge invariance, gauge
transformations and gauges, homogeneous Maxwell equations Lagrange Mechanics of Fields: Euler-Lagrange equations, real scalar field, |
[manu-script
EDFT 21-30] [Brau, chap. 2.2] [Lan2, chap. 15-18,23-24] [Jack, chap. 11.10, 12.1] |
Problem
sheet 2 due 1 Feb |
26 Jan, Thu lecture 4 |
Noether's
theorem on conserved currents and the energy-momentum tensor; Lagrangean of Electrodynamics and Maxwell's equations continuity equation; energy-momentum tensor, Poynting's vector and Maxwell's stress tensor; energy-momentum tensor, Poynting's vector and Maxwell's stress tensor |
[manu-script
EDFT 31-39] [Brau, chap. 2.3-4] [Lan2, chap. 26-33] [Jack, chap. 12.7, 10] |
. |
31 Jan, Tue lecture 5 |
outlook:
Beyond
Classical Fields (not examinable) matter fields, photon mass and supercondcutivity, magnetic monopoles |
[manu-script EDFT 40-45] | Problem
sheet 3 due 8 Feb Handouts: Superconductivity Magnetic Monopoles |
2 Feb, Thu lecture 6 |
Electrostatics
(2 lectures) Poisson equation, potential energy of charge distributions, Recaps: elementary solution by a Green's function (uniqueness, boundary conditions), formal solution of electrostatic problems, method of image charges, Recaps: multipole decomposition of boundary value problems in spherical coordinates, Legendre polynomials and spherical harmonics; spherical multipole moments of the potential and energy in an external field; example(s) Link to a Java-Applet plotting Spherical Harmonics advantages of (spherical) multipoles; Review CONS: more complete systems of orthonormal functions; Bessel functions; general eigenfunction expansion of Green's functions |
[manu-script EStat
1-10,16-27, 32-35] Mathematica Methods lecture [M, chap 8.1/3/7,9.4,12.4-6, 12.8 ] [Brau, chap. 3.1.1-2, 3.2] [Jack, chap. 1.7-1.11, 2.1-6,2.8,3.5-6, 4.1-2] cursorily: [Jack, chap. 3.7-9, 3.11] all of the above, [Jack, chap. 3.12] cursorily: [Jack, chap. 3.7-9, 3.11] [M, chap. 9.5] |
Handouts: Suplement on Spherical Harmonics (from Math. Meth.) Suplement on Fourier Transforms (from Math. Meth.) |
7 Feb, Tue lecture 7 will happen as scheduled |
Cartesian multipole moments of charge distributions, fields and potentials: monopole, dipole and quadrupole; interpreting the dipole; dipole with image charges | [manu-script
EStat 11-15, 28-31] [Brau, chap. 3.1.3] [Lan2, chap. 40-42] (only readable account on Cartesian multipoles) [M, chap. 9.5] |
Problem
sheet 4 due 15 Feb |
9 Feb, Thu lecture 8 |
Magnetostatics
(1lecture) law of Biot-Savart, vector potential; magnetic dipole and its moment; magnetic pseudo-potential, hyperfine splitting, Larmor precession |
[manu-script MStat 1-11] [Brau, chap. 3.3, 6.2.2] [Lan2, chap. 43-45] [Jack, chap. 5.1-7] |
. |
14 Feb, Tue lecture 9 moved to Thu 16 Feb at 17:00 |
Some
Review/Breathing Space: Relativity, Electrostatics and Magnetostatics In-class problem set I |
. | Problem
sheet 5 due 22 Feb |
16 Feb, Thu lecture 10 |
Radiation
and Radiating Systems (7 lectures) free radiation: solution of the equations of motion, plain, mono-chromatic wave, energy and momentum of the free wave, polarisation (linear, elliptic, circular) |
[manu-script RadSys 1-7] [Brau, chap. 4.1] [Lan2, chap. 46-51] [Jack, chap. 7.1-2] |
. |
21 Feb, Tue lecture 11 |
group-
and
phase-velocity; very brief recap on Complex Analysis; Green's function of the wave-equation with sources: Helmholtz', retarded, advanced, Feynman's Green's function; retarded potentials |
[manu-script RadSys 8-16] [Lan2, chap. 62] [Jack, chap. 6.2-4] [M, chap. 8.7., esp. example 8.7.2] |
Problem
sheet 6 due 1 Mar |
23
Feb, Thu lecture 12 |
retarded
potentials: example; radiation of electromagnetic waves: near-field zone, intermediate zone, far-zone: electric & magnetic fields, radiated power Movies of Hertz' dipole (Hsiu Han, Iowa State): radiation, E-field & B-field pattern, power radiated Mathematica animation: Hertz' dipole |
[manu-script
RadSys 17-20] see above [Lan2, chap. 64,66] [Brau, chap. 10.1] [Jack, chap. 9.1] |
. |
28 Feb, Tue lecture 13 |
long-wavelength
approximation; Hertz's electric dipole; magnetic
dipole radiation; electric
quadrupole radiation |
[manu-script
RadSys 21-28a] see above [Lan2, chap. 67,71] [Jack, chap. 9.2-4] |
Problem
sheet 7 due 8 Mar. |
2 Mar, Thu lecture 14 |
dimensional
analysis of the radiation power of
multipoles; exact multipole
expansion of the radiation field In-class problem II |
[manu-script
RadSys 29-34] [Jack, chap. 9.6-11] |
Problem
sheet 8 special due date Mon 20 Mar 09:00 (last for midterm). |
7 Mar, Tue lecture 15 |
radiation
from accellerated charges: Lienard-Wiechert potentials,
radiation loss by Larmor's (relativistic) formula, radiation
characteristics: angular
distribution and spectrum illustrating field-lines: Tsien: Am. J. Phys. 40 (1972), 46 |
[manu-script
RadSys 35-40] [Lan2, chap. 63, 69, 73-74] [Brau, chap. 10.1/2.1] [Jack, chap. 14.1-6] |
. |
9 Mar, Thu lecture 16 |
synchrotron
radiation; bremsstrahlung |
[manu-script
RadSys 41-43] see above slides with movies [Brau, chap. 10.4] [Jack, chap. 15.1&6] |
. |
14/16 Mar | No lectures (Spring Break) | ||
20 Mar, Mon special date & time 16:00 |
Surgery Hour for HWs 1-8 |
||
21 Mar, Tue lecture 17 |
Lecturer's
Question Time (please indicate possible topics beforehand) |
Up to and including multipoles of Radiating Systems | Problem
sheet 9 due 29 Mar. |
22 Mar, Wed | 8:30
sharp - 10:30, Staughton 103
Mid-Term Exam: 2:00 hours, closed-book, sheet with mathematical formulae provided. |
||
23
Mar, Thu lecture 18 |
Scattering
Theory of Radiation (2 lectures) boundary conditions for scattering, scattering amplitude, cross-section, dipole approximation; scattering off a harmonically bound charge: Lorentz oscillator model, electric polarisability, Thomson limit, resonance fluorescence, Rayleigh-scattering: Why the sky is blue |
[manu-script Scatt 1-8] [Jack, chap. 10.1-2, 16.8, 14.8] [Brau, chap. 10.3.1] [Lan2, chap. 78-80] (radiation loss: [Lan2, chap. 75-76], [Jack, chap. 16.7]) |
. |
28 Mar, Tue lecture 19 |
polarisation
of scattered waves; coherent and incoherent scattering |
[manu-script Scatt 9-15] see above [Jack, chap. 10.1, 16.8] . |
Problem
sheet 10 due 5 Apr. |
30 Mar, Thu lecture 20 |
Electrodynamics
in Matter (9 lectures) deriving Maxwell's equations in media by averaging charge and current distributions, macroscopic and microscopic fields |
[manu-script Media 1-7] [Brau, chap. 6.1.1-2] [Jack, chap. 4.3, 4.7, 5.8, 5.16, 6.6-8] [Jack] for media is a mess, scattering (pun intended) material all over the book |
. |
4 Apr, Tue lecture 21 |
energy balance in media; boundary conditions for homogeneous, isotropic, linear media: examples tilted plate (refraction of field lines), point-charge in front of medium; linear electric response, ferroelectrica | [manu-script
Media 8-14] [Brau, chap. 6.1.3] [Jack, chap. 4.4, 5.9] |
Problem
sheet 11 due 12 Apr Movies on parallel-plate waveguide (Hsiu Han, Iowa State): TE1 mode above/at/below crit. frequency, range of frequencies, TE2 mode above/below crit. frequency. |
6 Apr, Thu lecture 22 |
linear electric response, its causality and approximations for an isotropic, local response function; dielectric function and electric susceptibility; Lorentz-Drude model for polarisability and dielectric function, high- and low-frequency limits (conductor, dielectric), Clausius-Mossotti relation, paraelectrica and orientation polarisation | [manu-script
Media 15-21] [Brau, chap. 6.2.1, 7.1.1/2] [Jack, chap. 4.5/6, 7.5, 7.10] |
. |
11
Apr, Tue lecture 23 moved to Wed 5 Apr at 16:00 |
analyticity
of the dielectric function:
Kramers-Kronig dispersion relations as examples of Dispersion
Relations/sum rules; magnetic response of media: magnetic susceptibility and permeability, dia-, para, ferro-, ferri-, anti-ferro-magnetism |
[manu-script
Media 22-24] see above [manu-script Media 25-29] [Brau, chap. 6.2.2] [Jack, chap. 5.10-13] |
Problem
sheet 12 due 19 Apr. |
13
Apr, Thu lecture 24 moved to Wed 19 Apr at 16:00 |
electromagnetic
waves in linear media: dispersion relation, plane-wave solution, index
of refraction,
damping/attenuation coefficient (see movies below), normal and
anomalous dispersion,
phase, group and signal velocity in media; Čerenkov-radiation |
[manu-script
Media 33-38, 50-51] [Brau, chap. 7.1.4-6] [Jack, chap. 7.8-9] see also our discussion on group and phase velocity |
|
18 Apr, Tue lecture 25 |
reflection
and refraction: laws for absorptive media, reflection and transmission
coefficients, total internal reflection, Brewster-angle Movies on refraction (Hsiu Han, Iowa State): vacuum-to-medium: with reflection, without reflection medium-to-vacuum: with reflection, without reflection, changing angle, at critical angle, total internal reflection Mathematica animations: Fresnel-equations, reflection & refraction between media |
[manu-script Media 39-44] [Brau, chap. 7.2] [Jackson, chap. 7.3-4] |
Problem
sheet 13 due 26 Apr. |
20 Apr, Thu lecture 26 |
dispersion
and absorption in insulators, metals and plasmas, skin-effect, opacity
and transparency of plasmas and metals Movies of waves (Hsiu Han, Iowa State): water (insulator), copper (good conductor), plasma |
[manu-script Media 45-49] [Brau, chap. 4.3, 7.1-2, 10.6] [Jack, chap. 7.5-6, 13.4] |
. |
25 Apr, Tue lecture 27 moved to Thu 27 Apr at 17:00 |
example
of medium in which the dielectric function is a tensor: Faraday
Rotation of linearly polarised beams in plasma with external static
magnetic field; from Scattering Theory of Radiation: emergence of geometrical optics |
[Brau,
exercises 4.18, 7.8] [manu-script Scatt 16-18] see above [Jack, chap. 10.1, 16.8] |
Problem
sheet 14 Special due date 1 May |
27 April, Thu lecture 28 |
More
weird examples Wrap-Up |
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. |
t.b.a. |
Lecturer's
Question Time (please indicate possible topics beforehand) |
. | .. |
8 May, Mon *NEW DATE* |
09:30
sharp - 12:00, Staughton 205
Final Exam: 2:30 hours, closed-book, sheet with mathematical formulae provided. |
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