Lastchanged 26 March 2017.
Changed final exam date.
Watchthis space for changes.
Changed final exam date.
Watchthis space for changes.
The book concludes by returning to basics, discussing the fundamental problems inherent in the classical theory of electrons. Modern Problems in Classical Electrodynamics features examples and homework exercises drawn from condensed-matter physics, particle physics, optics, and atomic physics. Many of these are experimentally oriented and help to make the book interesting and relevant to a.
Lectures: Tuesday, Thursday 12:20to 14:00 in Staughton 103.All lectures are 100minutes, equivalent to 4 credit hours.
'Snow Days' (if we need toreschedule 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 14:00inStaughton 103. Laststill all questions are answered.
Homework Due: Wednesdays at16:00hrs. Zero points for assignments not turned inon time, unless you notify me before the due date with reproducibly legitimate reasons (e.g.~illness).
Homework Due: Wednesdays at16:00hrs. Zero points for assignments not turned inon time, unless you notify me before the due date with reproducibly legitimate reasons (e.g.~illness).
Additionaloffice hoursby appointment after 3pm in my office. Email what and when to discuss.
email: hgrie<at> gwu.edu
email: hgrie<at> gwu.edu
Audience
First-year graduate students.
Goals
Introduction into the theoretical concepts and mathematicalmethods of Classical Electrodynamics as example of a relativistic FieldTheory. Focus on skill-building, symmetry principles, controlledapproximations, and concepts at the fore-front of research.
An incomplete, over-achieving, informal list of Questions to Check YourProgresscan be found here.Under no condition is this a survey of material for exams -- neithermaximal nor minimal. It might not even be of any use at all.
Prerequisites
Undergraduate Electrodynamics on thelevel of Griffith: Introductionto Electrodynamics,Chaps. 1-6;advanced undergraduate mathematical methods; undergraduate QuantumMechanics.
The graduate courses in Autumn, in particular PHYS 6110:Mathematica Methods of Theoretical Physics and thechapterson Lagrangean Mechanics and Relativity in PHYS 6120:Classical Mechanics,areindispensable. See the first two paragraphs in the Questions to Check YourProgress.
Co-requisite
PHYS 6230:Computational PhysicsII (Haberzettl/Griesshammer).
Coordinated with: PHYS 6220:Quantum MechanicsI (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 8:30to 10:30 in Staughton 103,2 hours;
- Final Exam (40% of total): Tuesday, 16 May 9:30 to 12:00 in Staughton 103, 2.5hours.
separately. In particular, you need at least 50% of all points in allProblem sheets together (not per sheet!). An excellent scoreusually starts at 80% of all points. Exams are closed-book.A sheet with some possibly relevant mathematical formulae will beprovided by me in the days before each exam.
Exercises/Homework
Problem sheets are onlineWednesdays andposted on this web-site (seebelow), due thefollowing Wednesday at 16:00am.Drop hardcopies in my pigeon-hole in the Physics office or fax to994-3001, or mail to hgrie <at>gwu.edu . No grace periodgranted.
Graded solutions are returned and discussed during the next Surgeryhour.
Handwrittensolutions must be on 5x5 quadrille ruled paper; electronic solutionsmust be in .pdf format.
Use of a 'lab-book' or'journal' for homework is strongly encouraged.
Contents (withlinks to manuscripts -- seeCaveat/Warning/Disclaimer)
- FundamentalEquations of Electrodynamics (1 lecture)
- Electrodynamicsas Relativistic Field Theory (3+1 lectures)
- Electrostatics(2 lectures)
- Magnetostatics(1 lectures)
- Radiationand Radiating Systems (7 lectures)
- ScatteringTheory (2+1 lectures)
- Electrodynamicsin Matter (9-1 lectures)
- AdvancedTopics (time permitting)
Syllabus: MoreInformation/Bibliography/Units/Conventions
The only authoritative version of the syllabus contains much moreinformation and is available as as .pdf-file: edyn.information.pdfFurther files: Conventionsused; EssentialMath and Physics formulae and numbers (what one needs to knowin one's sleep).
![Modern problems in classical electrodynamics pdf Modern problems in classical electrodynamics pdf](/uploads/1/2/5/7/125799745/707453911.jpg)
Bibliography
There is norequired reading for this course. You will not be able tofind all aspects of the lecture explained well in only one textbook.Moreover, it is an essential part of the learning process to view thesame topic from different angles, i.e. using differenttextbooks. Here is a list of those which I found most useful.If you discover others, tell me.
The Classschedule lists for each lecture recommended readings.
Anasterisk * indicates titles on Course Reserve at GelmanLibrary, 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$. Not necessarily the best choice...
On Theoretical Electrodynamics:
- [Brau]* Ch.A. Brau: Modern Problems in Classical Electrodynamics; OxfordUniversity Press; ca. 98$. Modern treatment, closely followscourse-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$.
- [Lan8]* L.D. Landau, E.M. Lifshitz andL.P. Pitaevskii: Electrodynamics of Continuous Media [Course ofTheoretical Physics Series, Vol.~8]; 2nd ed., Butterworth-Heinemann;ca. 45$.
- [Jack] * J.D. Jackson: ClassicalElectrodynamics; 3rd ed., John Wiley, ca. 100$. List of errata at http://www-theory.lbl.gov/jdj/Errata-%2702-%2708.pdf.
- [Grif] D.J. Griffith: Introduction toElectrodynamics; 3rd ed., Prentice Hall; ca. 102$.
- [Schwa] M. Schwartz: Principles ofElectrodynamics; Dover; ca. 12$.
[Ein1] Link toannotated English translations Einstein's paper of the Annus Mirabilis1905;anotherlink 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'sTheory of Relativity; Dover.
LectureManuscript
A scanned version of a chapter-by-chapter manuscript can befoundby following the links of chapter headings in the ClassSchedule and Contents Section.The files are in .djvu-format, which is at present the most condensedwayof storing scanned images: 50 scanned pages translate into 1.2 Gbytesof bitmap, or 50 MBytes .pdf or 4.7 MBytes of .djvu. The freeware djvureader '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 ofthe Physics presented, this script bears only witness of my limitedunderstanding of the subject. I am most grateful to every reader whocan point out typos, errors, omissions or misconceptions. Maybe overthe years, with lots of student participation, this can grow intosomething remotely useful.
The script only intends to ease the pain of following thelecture, and doesnot replace the thorough study of textbooks.
The script is notintended to be comprehensible,comprehensive -- or even useful.
It is certainly not legible.
Your mileage will vary.
Thisscript is not useful or relevant for exams of any kind.
BestPractice
Read over the manuscript before class. Try tograsp theessential points. The better prepared you are, the more we can focuson discussing your questions and observations, and solve problems. Theclassbecomes more interactive and thus more fun -- and therefore you learnmore.
Study details of the manuscript after the lecture, and follow thederivation of all formulae line-by-line. This is excellent and freeexercise for your math skills, and makes sure you not just 'read long'.It is also the starting pointfor your own literature research using good books like thoserecommended for particular subjects in the 'Suggested Reading' columnbelow.
Class Schedule (noexact match, but an outlinehow we hope to progress)
Date | Topics (linkto .djvu-file with manuscript) | SuggestedReading | Exercises |
. | Revisityourundergraduate course notes. Revisit your Mathematical Methods course notes, in particular: partialdifferential 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 onSpecial Relativity. | See the first two paragraphs intheQuestionsto 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 FundamentalEquations of Electrodynamics (1 lecture) recap: Interpretation of Maxwell's equations, Poisson equation, Gauss',Stokes' and Helmholtz'theorems, scalar and vector potentials, conventions Electrodynamicsas Relativistic Field Theory (3+1 lectures) recap Special Relativity: postulates, Lorentz transformations, co- andcontra-variant 4-vectors, | [manu-script Fundamentals] MathematicalMethods 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] Mechanicslecture [Brau, chap.1.1-3, 2.1] [Lan2, chap. 1-9] [Jack, chap. 11.1-4,6-8] see also [Ein1, Ein2, Ein3, Born] | Problemsheet 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 | relativisticmechanics of pointparticles Link tonice visualisations of relativistically moving objects (lookfor 'Film Index' and 'First-Person Visualisations'; partially in German) particlein external4-vector gauge field, electric and magnetic fields from thefieldstrength tensor; | [manu-script EDFT 5-20] see above | |
24 Jan, Tue lecture 3 | electricandmagnetic fields from thefieldstrength tensor (cont'd); Lorentz-transformationof electric and magnetic fields, gauge freedom, gauge invariance, gaugetransformations and gauges, homogeneous Maxwell equations LagrangeMechanics of Fields: Euler-Lagrange equations, real scalar field, | [manu-scriptEDFT 21-30] [Brau,chap.2.2] [Lan2, chap. 15-18,23-24] [Jack, chap. 11.10, 12.1] | Problemsheet 2 due 1 Feb |
26 Jan, Thu lecture 4 | Noether'stheorem on conserved currents and the energy-momentum tensor; Lagrangeanof Electrodynamics and Maxwell's equations continuity equation; energy-momentumtensor,Poynting's vector and Maxwell's stress tensor; energy-momentumtensor,Poynting's vector and Maxwell's stress tensor | [manu-scriptEDFT 31-39] [Brau, chap.2.3-4] [Lan2, chap. 26-33] [Jack, chap. 12.7, 10] | . |
31 Jan, Tue lecture 5 | outlook:BeyondClassical Fields (not examinable) matter fields, photon mass and supercondcutivity, magnetic monopoles | [manu-script EDFT 40-45] | Problemsheet 3 due 8 Feb Handouts: Superconductivity MagneticMonopoles |
2 Feb, Thu lecture 6 | Electrostatics (2 lectures) Poisson equation, potentialenergy of charge distributions, Recaps: elementary solution by aGreen'sfunction (uniqueness, boundaryconditions), formalsolution of electrostatic problems, method ofimage charges, Recaps: multipole decomposition of boundary valueproblems in sphericalcoordinates, Legendre polynomials and sphericalharmonics; sphericalmultipole moments of the potential and energy in an externalfield; example(s) Linkto a Java-Applet plotting Spherical Harmonics advantagesof (spherical) multipoles; Review CONS: morecomplete systems of orthonormalfunctions; Bessel functions; general eigenfunction expansion of Green'sfunctions | [manu-script EStat1-10,16-27, 32-35] MathematicaMethods lecture [M, chap8.1/3/7,9.4,12.4-6, 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] allof theabove, [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 | Cartesianmultipole moments of charge distributions, fieldsand potentials: monopole, dipole and quadrupole; interpreting thedipole; dipole with image charges | [manu-scriptEStat 11-15, 28-31] [Brau,chap.3.1.3] [Lan2, chap. 40-42] (only readable account on Cartesian multipoles) [M, chap. 9.5] | Problemsheet 4 due 15 Feb |
9 Feb, Thu lecture 8 | Magnetostatics (1lecture) law of Biot-Savart, vector potential; magnetic dipole and itsmoment; magneticpseudo-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 | SomeReview/Breathing Space: Relativity, Electrostatics and Magnetostatics In-class problem set I | . | Problemsheet 5 due 22 Feb |
16 Feb, Thu lecture 10 | Radiationand Radiating Systems (7 lectures) freeradiation: solution of the equations of motion, plain, mono-chromaticwave, 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-andphase-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] | Problemsheet 6 due 1 Mar |
23Feb, Thu lecture 12 | retardedpotentials: example; radiationof electromagnetic waves: near-field zone, intermediate zone, far-zone:electric & magnetic fields, radiated power Moviesof Hertz' dipole (HsiuHan, Iowa State): radiation,E-field & B-fieldpattern, powerradiated Mathematicaanimation: Hertz'dipole | [manu-scriptRadSys 17-20] see above [Lan2, chap.64,66] [Brau, chap. 10.1] [Jack, chap. 9.1] | . |
28 Feb, Tue lecture 13 | long-wavelengthapproximation; Hertz's electric dipole; magneticdipole radiation; electricquadrupole radiation | [manu-scriptRadSys 21-28a] see above [Lan2, chap.67,71] [Jack, chap. 9.2-4] | Problemsheet 7 due 8 Mar. |
2 Mar, Thu lecture 14 | dimensionalanalysis of the radiation power ofmultipoles; exact multipoleexpansion of the radiation field In-class problem II | [manu-scriptRadSys 29-34] [Jack, chap. 9.6-11] | Problemsheet 8 special due date Mon 20 Mar 09:00 (last for midterm). |
7 Mar, Tue lecture 15 | radiationfrom accellerated charges: Lienard-Wiechert potentials,radiation loss by Larmor's (relativistic) formula, radiationcharacteristics: angulardistribution and spectrum illustrating field-lines: Tsien:Am. J. Phys. 40 (1972), 46 | [manu-scriptRadSys 35-40] [Lan2, chap.63, 69, 73-74] [Brau, chap. 10.1/2.1] [Jack, chap. 14.1-6] | . |
9 Mar, Thu lecture 16 | synchrotronradiation; bremsstrahlung | [manu-scriptRadSys 41-43] see above slides with movies [Brau, chap. 10.4] [Jack, chap. 15.1&6] | . |
14/16 Mar | Nolectures (Spring Break) | ||
20 Mar, Mon special date & time 16:00 | Surgery Hour for HWs 1-8 | ||
21 Mar, Tue lecture 17 | Lecturer'sQuestion Time (please indicate possible topics beforehand) | Upto and including multipoles ofRadiating Systems | Problemsheet 9 due 29 Mar. |
22 Mar, Wed | 8:30sharp - 10:30, Staughton 103 Mid-Term Exam: 2:00 hours, closed-book, sheet with mathematical formulae provided. | ||
23Mar, Thu lecture 18 | ScatteringTheory of Radiation (2 lectures) boundary conditions for scattering, scattering amplitude,cross-section, dipole approximation; scattering off a harmonicallybound 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 | polarisationof scattered waves; coherent andincoherent scattering | [manu-script Scatt 9-15] seeabove [Jack, chap.10.1, 16.8] . | Problemsheet 10 due 5 Apr. |
30 Mar, Thu lecture 20 | Electrodynamicsin Matter (9 lectures) deriving Maxwell's equations in media by averaging charge and currentdistributions, 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 thebook | . |
4 Apr, Tue lecture 21 | energybalance in media; boundaryconditions for homogeneous, isotropic, linear media: examples tiltedplate (refraction of field lines), point-charge in front ofmedium; linearelectric response, ferroelectrica | [manu-scriptMedia 8-14] [Brau, chap. 6.1.3] [Jack, chap. 4.4, 5.9] | Problemsheet 11 due 12 Apr Movieson parallel-plate waveguide (HsiuHan, Iowa State): TE1 mode above/at/belowcrit. frequency, rangeof frequencies, TE2 mode above/belowcrit. frequency. |
6 Apr, Thu lecture 22 | linearelectric response, its causality and approximations for anisotropic, local response function; dielectric function and electricsusceptibility; Lorentz-Drudemodel for polarisabilityand dielectric function, high- and low-frequency limits (conductor,dielectric), Clausius-Mossottirelation, paraelectricaand orientation polarisation | [manu-scriptMedia 15-21] [Brau, chap.6.2.1, 7.1.1/2] [Jack, chap. 4.5/6, 7.5, 7.10] | . |
11Apr, Tue lecture 23 moved to Wed 5 Apr at 16:00 | analyticityof the dielectric function:Kramers-Kronig dispersion relations as examples of DispersionRelations/sum rules; magnetic response of media: magnetic susceptibility andpermeability, dia-, para,ferro-, ferri-, anti-ferro-magnetism | [manu-scriptMedia 22-24] see above [manu-script Media 25-29] [Brau, chap. 6.2.2] [Jack, chap. 5.10-13] | Problemsheet 12 due 19 Apr. |
13Apr, Thu lecture 24 moved to Wed 19 Apr at 16:00 | electromagneticwaves in linear media: dispersion relation, plane-wave solution, indexof refraction,damping/attenuation coefficient (see movies below), normal andanomalous dispersion,phase, group and signal velocity in media; Čerenkov-radiation | [manu-scriptMedia 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 | reflectionand refraction: laws for absorptive media, reflection and transmissioncoefficients, total internal reflection, Brewster-angle Movieson refraction (HsiuHan, Iowa State): vacuum-to-medium:withreflection, withoutreflection medium-to-vacuum:withreflection, withoutreflection, changingangle, atcritical angle, totalinternal reflection Mathematicaanimations: Fresnel-equations, reflection& refraction between media | [manu-script Media 39-44] [Brau, chap.7.2] [Jackson, chap. 7.3-4] | Problemsheet 13 due 26 Apr. |
20 Apr, Thu lecture 26 | dispersionand absorption in insulators, metals and plasmas, skin-effect, opacityand transparency of plasmas and metals Moviesof waves (HsiuHan, 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 | exampleof medium in which the dielectric function is a tensor: FaradayRotation of linearly polarised beams in plasma with external staticmagnetic field; from ScatteringTheory of Radiation: emergence of geometrical optics | [Brau,exercises 4.18, 7.8] [manu-scriptScatt 16-18] seeabove [Jack, chap.10.1, 16.8] | Problemsheet 14 Special due date 1 May |
27 April, Thu lecture 28 | Moreweird examples Wrap-Up | . | . |
t.b.a. | Lecturer'sQuestion Time (please indicate possible topics beforehand) | . | .. |
8 May, Mon *NEW DATE* | 09:30sharp - 12:00, Staughton 205Final Exam: 2:30 hours, closed-book, sheet with mathematical formulae provided. | . | .. |