1. Homework
    1. HW12 is due Tuesday December 1st.
    2. HW13 will not be collected, but is most probably part of the final. The solutions are already below.
  2. Final Exam:
    1. This year's midterm and solutions are exam and solutions
    2. This years final exam and solutions are exam and solutions
    3. The exam will cover everything since the midterm, i.e. retarded Green functions to the end.
    4. The exam covers hw9 -- hw13 with a bit of hw8.
    5. The past two final exams are exam2_2013 and exam2 2014. The solutions are here and here.
    6. The 2014 exam was notably harder than the 2013 exam, and was to a degree less successful.
  3. Please find the relativity lecture notes one line problems in relativity notation
  4. Please find the following hopefully helpful notes
    1. Notes on Green functions and Green theorem
    2. Notes on retarded time
  5. The course page for Fall 2014 can provide a qualitative guide to this years structure:

Course Summary

Course Summary

Week 1: 8/25 Introduction and Electrostatics:
Week 2 : 9/1 Mathematics of the Poisson Equation:
Week 3 : 9/8 Mathematics of the Poisson Equation (continued)
Week 4: 9/15 Chapter 4: Electrostatics in Material
Week 5: 9/16 Currents and Ohms Law. Magnetostics
Week 6: 9/29 Quasistatics fields
Week 7: 10/6 Conservation Laws. Waves. Propagation of waves at interfaces:
Week 9: 10/21 Multipole radiation and radiation from slow charges : non-relativistic radiation
Week 10: 10/28 Relativity and Electrodynamics: relativity part i
Week 11: 11/3 Relativity and Electrodynamics continued relativity part ii
Week 12: 11/10 Radiation from relativistic charges relativistic radiation part i
Week 13: 11/17 Radiation from relativistic charges continued relativistic radiation part ii
Thanksgiving week Class Monday, then break
Week 14: 12/2 Scattering scattering

Homework and Solutions

Week 1: hw1, hw1_sol
Week 2: hw2, hw2_sol
Week 3: hw3, hw3_sol
Week 4: hw4, hw4_sol
Week 5: hw5, hw5_sol
Week 6: hw6, hw6_sol
Week 7: hw7, hw7_sol
Week 8,9: hw8,hw8_sol
Week 10: hw9, hw9_sol
Week 11: hw10, hw10_sol, hw10_inclass, hw10_inclass_sol
Week 13: hw11, hw11_sol
Week 14: hw12, hw12_sol, and hw13, hw13_sol

Lecture Notes and Tentative Schedule

Week 1: 8/25 The Maxwell equations and mathematical review:
  1. Units
  2. Overview: Specify the currents (or a constituent relation) and solve for the fields
  3. Vector analysis, tensors, "bac-abc", Helmholtz theorems and immediate applications:
    • Gauge invariance
    • current conservation
    • Waves
  4. Expansion of the Maxwell equations in 1/c
  1. Fundamental equations and boundary conditions
  2. Electrostatic energy
  3. Stress and force in electrostatics:
    • The stress tensor and forces generally, momentum conservation law
    • The electric stress tensor and two in class problems
  4. The multipole expansion
  5. Forces on a multipole
Week 2: 9/1 Methods of Electrostatics
  1. Intro to Green Functions and Image Charges
  2. Green Theorem
    • Example
    • Proof
  3. Separation of Variables for BVP
  4. A charged ring in a sphere
  5. A charged cylindrical shell and modified bessel functions
Week 3: 9/8 Week 2 continued
Week 4: 9/15 Electrostatics in Material:
  1. A consitutive relation for the current in electric fields
    • Determining the current -- the polarization vector
    • The material charge density in the bulk and interfaces
    • Relation to the dipole picture
  2. Boundary value problems with dielectrics
  3. Energy and stress in dielectrics
  4. Ohms Law and steady currents
Week 5: 9/22 Magnetostatics
  1. Basics
    • Expansion of the Maxwell Equations in 1/c
    • Amperes Law and Biot Savat
    • Gauge Potentials and the Coulomb Gauge
  2. Magnetic Multipoles
    • Field from a multipole
    • Force and torque on a multipole
  3. Boundary conditions in magnetostatics
    • Boundary conditions
    • a spinning sphere
  4. Magnetic Fields in matter:
Week 6: 9/29 Quasi-statics in vacuum and metals. Maxwell Equations for Potentials.
  1. Basics of Induction:
    • The maxwell equations expansion to 1/c^2
    • Energy stored in magnetic field.
    • Mutual inductance
  2. The Maxwell equations for the gauge potentials and quasistatics.
  3. Quasi-static fields in metals
Week 7: 10/6 Conservation Laws. Propagation of waves in media and interfaces:
  1. Conservation Laws
  2. Basics of Waves
  3. Reflection at Interfaces
  4. Waves in Metals and Reflection
Week 8: 10/13 Dispersion. Wave packtes.
  1. Linear response. Waves in dispersive media
  2. Lorentz model for insulators and metals
  3. Wave packets, group velocity, and phase shifts
  4. Kramers Kronig relations
Week 9: 10/20 Retarded Green Functions.
  1. Simple Harmonic Oscillator
  2. The wave equation
  3. Green theorem notes
Week 10: 10/27 Multipole radiation and radiation from slow charges.
  1. Radiation fields, and technical note
  2. Larmour formula and electric dipole radiation
  3. Magnetic dipole and quadrupole radiation
  4. Antennas
Week 11: 11/3 Relativity and Electrodynamics:
  1. Introduction and Manifest Covariance. In-class problems
  2. Electrodynamics in Covariant Form:
    • The sourced (i.e. current driven) Maxwell equations
    • The unsourced Maxwell equations and the Bianchi identity
    • The stress tensor
    • One line problems.
  3. Transformations of fields.
    • Fields of fast particles
    • Constituent relations of moving bodies
  4. Relativistic action and Hamiltonian for particles.
  5. Relativistic action for the fields.
Week 12: 11/10 Radiation from relativistic charges:
  1. The fields of point particle
    • Lienard-Wiechert potentials and fields.
    • The power during radiated by relativistic charged particles.
    • Circular versus Linear Accelerators.
  2. The frequency spectrum in relativistic radiation, with applications to synchrotron radiation.
    • The frequency spectrum associated with relativistic charged particles
    • Qualitative estimates of synchrotron radiation.
    • Quantitive calculations of sychrotron radiation.
  3. The bremsstrahlung spectrum
    • The spectrum of photons accompanying a collision.
    • Number of photons in a bremsstrahlung cone.
    • Number of bremsstrahlung photons with a given polarization.
Thanksgiving: 11/24 Scattering and Diffractioon
Week 14: 12/1 Scattering and Diffraction
  1. Overview
    • Cross sections
    • The Thompson cross section and associated polarizations
  2. Dipole scattering
  3. Born approximation

Course Organization


This is an intense one semester graduate course in Classical Electrodynamics. This is the only graduate course to meet 5 hours per week, and therefore graduate students should expect that this course will constitute a significant part of their first semester workload.

We begin with a very brief review of electrostatics and magnetostatics where the required special functions and Green function techniques are introduced. After this introduction, we describe Faraday's Law and the quasi-static approximation to the Maxwell system. Following these developments we study the propagation of light in media, and categorize the response functions of typical materials. Subsequently we describe diffractive and scattering phenomena with partially coherent light. Then we discuss multipole radiation, placing classical electrodynamics within the context of special relativity. This formalism is used to study radiation in various contexts. The course will emphasize problem solving.

A detailed set of scanned lecture notes and typed formulas will be provided for the course. Examples of the format of these notes is given on the course page for Fall 2014:

http://tonic.physics.sunysb.edu/~dteaney/F14_Phy505/course.htm .

The structure and tentative order of the course is the following

  1. The Maxwell Equations:

  2. Electrostatics:

  3. Electric fields in matter:

  4. Magnetostatics:

  5. Magnetism and magnetic fields in matter:

  6. The Maxwell equations and the quasistatic approximation:

  7. Propagation of waves in media and at interfaces:

  8. Multipole radiation, and radiation by slow charges:

  9. Relativity, covariance, and electrodynamics:

  10. Radiation by fast charges:

  11. Scattering of radiation and diffraction:

The following is a portrait of Faraday. May his memory inspire young experimentalists, and young theorists to listen to them.

Lecture Instructor:

Assoc. Professor, Derek Teaney: derek.teaney stonybrook.edu

Derek Teaney
Department of Physics & Astronomy
PO Box 3800
Stony Brook, NY 11764-3800

Office: Physics C-135

(631)632-4489, Fax 9718

Teaching Assistant, Yao Ma: yao.ma stonybrook.edu


Class Meetings

The course consists of three lecture hours and two hour recitation. Recitations will be used to discuss problems.

Office Hours

Please feel free to contact me at anytime. My official office hours are,

Final Exam

The final exam is on Tuesday, December 15 from 2:15--5:00 p.m in Harriman Hall 116.

Grade Determination

The grading will be based roughly on the following table. I reserve the right to change these proportions (within reasonable limits) as the course progresses. My intent of course is to follow these guidelines.

Homework 25%
Midterm Exam 35%
Final Exam 40%

Homework is a major part of this course, and students should expect approximately 8-10 hours of work per week. Homeworks will be assigned weekly, and will be collected ** at the start of class ** . Homework handed in within a day after the due date/time will by given a 5% penalty. After this, late homeworks will be penalized at 10% per day.

The Book and Resources

The required book for the course is

  1. Classical Electrodynamics by John David Jackson

Some other books which I used when preparing the course are:

  1. A good source of problems is: Modern Electrodynamics by Andrew Zangwill.
  2. A interesting perspective on the subject is: Classical Electrodynamics by Julian Schwinger, Lester Deraad, Kimball Milton, Wu-yang Tsai.
  3. Professor Likharev's Essential Graduate Physics
  4. I have found: Methods of Theoretical Physics, Part I and II by Morse and Freshbach an invaluable, enjoyable, and surprisingly readable reference over the years.

Other Items


Email to your University email account is an important way of communicating with you for this course. For most students the email address is firstname.lastname@stonybrook.edu, and the account can be accessed here: http://www.stonybrook.edu/mycloud". It is your responsibility to read your email received at this account.

For instructions about how to verify your University email address see this: http://it.stonybrook.edu/help/kb/checking-or-changing-your-mail-forwarding-address-in-the-epo. You can set up email forwarding using instructions here: http://it.stonybrook.edu/help/kb/setting-up-mail-forwarding-in-google-mail. If you choose to forward your University email to another account, we are not responsible for any undeliverable messages.

Disability Support Services (DSS):

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.

Academic Integrity:

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html

Critical Incident Management Statement:

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.

Assessment of Student Performance:

Professional Conduct and Interaction with Students: