Electromagnetic Theory: Lecture Log

January 17 (Wednesday):

Syllabus and admin: course content, textbook, prerequisites, homework, exams, grades, etc. (see the main web page for the class).
Methods of solving Laplace or Poisson equations for the Φ(x): image charges; separation of variables in rectangular and in spherical coordinates.

January 22 (Monday):

Green's functions and their uses: inverse operators; Dirichlet and Neumann boundary conditions; Green's function for the half-space; finding Φ(x) inside some volume given Φ or E_normal on the boundary; example.
Multipole expansion: expanding the potential of a compact charge distribution into power of 1/r; angular dependence and multipole tensors; formal construction of the multipole tensors; dipole moment vector in detail; quadrupole moment tensor in detail.

January 24 (Wednesday):

Multipole expansion: octupoles and the octupole moment tensor; higher multipole moments and their tensor structures; spherical harmonics for the multipoles.

January 29 (Monday):

Electric currents: charge conservation and the contonuity equations; steady currents.
Highlights of magnetostatics (my notes): Biot–Savart–Laplace Law and Ampere's Force Law; Newton's Third Law for magnetic forces; field equations for the magnetic field, Ampere's circuital law; vector potential A(x) and gauge transforms; equations for the vector potential and their solution; examples.
Started magnetic multipole expansion (my notes): the expansion; no monopole term; the dipole term in detail.

January 31 (Wednesday):

Magnetic dipoles (my notes): Dipole moment of volume currents; the dipole field; force and torque on a magnetic dipole in an external field.

Extra lecture on January 31 (Wednesday):

Classical and quantum mechanics of a charged particle (my notes): Classical Lagrangian and equations of motion; classical Hamiltonian; quantum Hamiltonian; gauge transforms and the local phase symmetry; generalization to quantum field theory.

February 5 (Monday):

Dielectric and magnetic materials (my notes): polarization, magnetization, and the macroscopic fields they create; the electric displacement field D the magnetic intensity field H; equations and boundary conditions for static electric and magnetic fields; dielectric sphere example; scalar magnetic potential Ψ; permanent magnet examples; multivalued Ψ(x) in presence of wires.

February 7 (Wednesday):

Electrostatic energy and forces on dielectrics.

Extra lecture on February 7 (Wednesday):

Aharonov–Bohm effect and magnetic monopoles (my notes):
Gauge transforms of propagation amplitudes; Aharonov–Bohm effect; cohomology of magnetic fluxes.
Magnetic monopoles via dummy magnets, Aharonov–Bohm effect, and charge quantization; Dirac's vector potentials for a monopole; Dirac's charge condition; monopoles in modern unified theories.

February 12 (Monday):

Magnetic energy and forces on magnetic materials (my notes).
Complex amplitudes and impedance.
Mutual inductance and transformers.

February 14 (Wednesday):

Eddy currents and skin effect (my notes).

February 19 (Monday):

Maxwell equations (my notes): the displacement current; Maxwell equations and electromagnetic waves; equations for the potentials A and Φ; Coulomb gauge; Landau gauge.
Green's functions of the d'Alembert operator (my notes): Fourier transformed Green's functions; causality, retarded and advanced Green's functions; retarded potential and retarded fields; Efimenko equations.
Electromagnetic energy: local conservation of energy; local work-energy theorem; EM energy density, flow density, and power density; Poynting vector and Poynting theorem.
Began EM momentum: local conservation of momentum; EM force density; EM momentum density.

February 21 (Wednesday):

Electromagnetic momentum: stress tensor in mechanics; stress tensor and momentum flow; Maxwell's stress tensor for EM fields; Pointing vector and momentum density; proof of local momentum conservation; pressure of EM radiation in a cavity.

February 26 (Monday):

EM power in dispersive media: time lag and complex ε(ω) and μ(ω); power dissipation due to Im(ε) and Im(μ); complex conductivity; attenuation of plane EM waves.
Microscopic origin of dispersion: single-resonance toy model; multi-resonance model; normal and anomalous dispersion; low frequency behavio: conductors vs insulators; high frequency behavior and plasma frequency; plasma frequency in metals.
EM wave absorption in water.

February 28 (Wednesday):

Dispersion in 1D waves: Phase velocity of a wave; wave packets and the group velocity; examples; refraction index; dispersion and spreading out of wave packets; signal rate.

Extra lecture on February 28 (Wednesday):

Electric–magnetic duality: E⇆B symmetry of Maxwell equations, energy, etc.; electric and magnetic charges and currents; charge quantization under duality; QCD analogy of electric-magnetic duality; quark confinement and chromomagnetic superconductivity.

March 5 (Monday):

Plane electromagnetic waves: wave vectors; electric and magnetic amplitudes; wave impedance; wave energy; linear, circular and elliptic polarizations; birefringerance and polarization rotation (briefly).
Reflection and refraction of electromagnetic waves (my notes): geometric laws for general waves: law of reflection and Snell's law of refraction; total internal reflection and evanescent waves.

March 7 (Wednesday):

Finished reflection and refraction of electromagnetic waves (my notes): boundary conditions for the EM waves; coefficients of reflection and transmission; calculations for waves polarized normally to the plane of incidence; calculations for waves polarized within the plane of incidence; Brewster's angle; phase shift in total internal reflection.

March 19 (Monday):

Symmetries of mechanics and electromagnetism: Rotations: scalar, vectors, and tensors; Reflections: polar and axial vectors, cross product rule, mechanical and EM examples, true scalars and pseudoscalars, parity; Time reversal symmetry: examples of T-even and T-off quantities.
Optical activity: chirality and birefringence; polarization rotation; Faraday affect; began Faraday effect in plasma; ionosphere example.

March 21 (Wednesday):

Finished Faraday effect in plasma; ionosphere example.
Began antennas and radiation: radiation by harmonic currents.
Gave out the midterm exam.

March 26 (Monday):

Antennas and radiation: near, intermediate, and far zones; spherical waves; multipole expansion.
Electric dipole approximation: the leading term and the electric dipole moment; H and E fields in the far zone; the radiated power and its direction dependence; dipole antenna example; atomic dipole radiation.

March 28 (Wednesday):

Magnetic dipole and electric quadrupole radiation: derivation, fields, net power, angular dependence.
Collect the midterm exam.

April 2 (Monday):

Finish electric quadrupole radiation (my notes): the net power and the direction dependence; radiateion pattern diagrams.
Radiation by a center-fed long linear antenna (my notes): general rules; standing current wave I(z); integral for the EM radiateion and its direction dependence; Examples of direction dependence for L/λ=½,1,2,3,4,6,10; general patterns; the net radiation power and the input impedance; antenna as a boundary problem.
Begin EM radiation by atoms: classical vs quantum radiation in the electric dipole approximation.

April 4 (Wednesday):

EM radiation by atoms and nuclei: selection rules for the electric dipole radiation; forbidden transitions and higher multipoles; selection rules for γ radiation in nuclei.
Introduction to scattering of EM waves: induced dipoles and scattered waves; polarized and un-polarized cross-sections.

Extra lecture on April 4 (Wednesday):

Superfluids: Bose--Einstein condensation and the condensate field; density and velocity of the superfluid.
Superconductivity: Cooper pairs and their condensation; the charged superfluid; Meissner effect; trapped magnetic flux and magnetic amplifiers.

April 9 (Monday):

Scattering of EM waves, examples: small dielectric sphere, small conducting sphere, free electron.
Multiple scatterers: interference and the form factor; Rayleight scattering by gases; Bragg scattering of X rays by crystals.

April 11 (Wednesday):

Origins of special relativity: Galilean relativity and its inconsistency with Maxwell equations; emission theory; aether theory; Fizeau experiment; aether wind, stellar aberrations, and Michelson–Morley experiment/

Extra lecture on April 11 (Wednesday):

Superconductivity: magnetic vortices; type II and type II superconductors.

April 16 (Monday):

Origins of special relativity: Michelson–Morley experiment; Lorentz contraction and time dilation; Einstein postulates.
Lorentz transforms and spacetime geometry (my notes): Lorentz transforms; relativistic velocity addition; Minkowski spacetime; intervals and lightcones; relativity of past and future; relativistic causality; proper time.

April 18 (Wednesday):

4–vectors: 4–vector notations and index rules; metric tensor and scalar product; O(3,1) group of boosts and rotations; derivative 4–vector, D'Alembert operator, and the wave equation.

April 23 (Monday):

Electrodynamics in a manifestly relativistic form (my notes): 4–current J^μ; 4–potential A^μ and gauge transforms; the F^μν tensor and the Lorentz transformation rules for the E and B fields; Lorentz covariant Maxwell equations; equations for the A^μ potentials; macroscopic Maxwell equations in a moving medium.
Relativistic momentum (my notes).

April 25 (Wednesday):

Relativistic energy and momentum (my notes): relativistic kinetic energy; non-conservation of mass and E=mc²; energy-momentum 4–vector p^μ and its square; relativistic center-of-mass energy in collisions.
Action formalism (my notes): free relativistic particle; charged particle in EM fields; covariant equation of motion and its 3D content.

Extra lecture on April 25 (Wednesday):

Superconductivity: Josephson junctions and SQUID magnetometers.

April 30 (Monday):

Action formalism (my notes): free relativistic particle; charged particle in EM fields; covariant equation of motion and its 3D content.
Radiation by moving charges (my notes): Liénard–Wiechart potentials; tension fields; Coulomb-like fields v. acceleration-dependent radition; radiated power.
EM power emitted by accelerating charges (my notes): Larmor formula and its relativistic generalization; synchrotron radiation; linacs v. synchrotrons.

Plan for May 2 (Wednesday):

Synchrotron radiation: angular distribution of radiation (my notes); frequency spectrum of synchrotron radiation; synchrotron X-ray sources.
Give out the final exam.