GW Department of Physics

Last changed 26 March 2017.

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: 

In order to pass, you need at least 60% of all points. You will also need at least 50% of the points available in each of the three components
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)

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.pdf
Further 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:

 More Background on Special Relativity/Historic Sources/Background:

            [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
.
.
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.
. ..