Electromagnetic Theory: Lecture Log

January 22 (Tuesday):

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 24 (Thursday):

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 29 (Tuesday):

Multipole expansion: dipole moment vector in detail; quadrupole moment tensor in detail; higher multipole moments and their tensor structures; spherical harmonics for the multipoles.

January 31 (Thursday):

Electric currents: charge conservation and the continuity 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.
Began magnetic multipole expansion (my notes): multipole expansion of A(x) due to for current is wires; vanishing of the monopole term; the dipole term.

February 5 (Tuesday):

Magnetic dipoles (my notes): Dipole moment of volume currents; the dipole field; forces and torques on magnetic dipoles; magnetic effects in atoms.
Macroscopic fields (my notes): space-averaged macroscopic E and B fields; polarization and magnetization in matter.

Extra lecture on February 6 (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 7 (Thursday):

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 12 (Tuesday):

Electrostatic energy and forces on dielectrics: electrostatic energy; self-energy and interaction energy; energy in linear and non-linear dielectrics; energy and forces in capacitors; forces on dielectrics in electric fields.

February 14 (Thursday):

Faraday's Induction Law (my notes: Faraday's flux rule; motional EMF; induced non-potential electric field; ∇×E=−∂B/∂t; scalar and vector potentials for dynamical fields.
Magnetic energy and forces on magnetic materials (my notes): energy of inductor coil; energy of magnetic field; energy loss to hysteresis; magnetic forces on materials.

February 19 (Tuesday):

Complex amplitudes and impedance.
Mutual inductance and transformers (briefly).
Eddy currents and skin effect (my notes): diffusion equation for the current and the magnetic field; solving the diffusion equation: how the field penetrates a conductor; skin effect for AC currents.

Extra lecture on February 20 (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 21 (Thursday):

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.

February 26 (Tuesday):

Electromagnetic energy: local conservation of energy; local work-energy theorem; EM energy density, flow density, and power density; Poynting vector and Poynting theorem.
Stress tensor: pressure and stress forces in continuous media; stress tensor; T_ij=T_ji; stress tensor and momentum flow; local conservation of momentum.
Electromagnetic momentum density, force density, and Maxwell's stress tensor; proof of local momentum conservation; pressure of EM radiation in a cavity.

February 28 (Thursday):

Finished Maxwell's stress tensor: anisotropy; pressure of disordered EM radiation.
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; attenuation and resonances; attenuation of EM waves in water.

March 5 (Tuesday):

Microscopic origin of dispersion: single-resonance toy model; multi-resonance model; normal and anomalous dispersion; low frequency behavior: conductors vs insulators; Drude conductivity in metals; high frequency behavior and plasma frequency; plasma frequency in metals.
Dispersion in 1D waves: phase velocity of a wave; wave packets and the group velocity; phase and group velocities in terms of the refraction index.

Extra lecture on March 6 (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.

March 7 (Thursday):

Finish dispersion in 1D waves (my notes): dispersion and spreading out of wave packets; signal rate.
Plane electromagnetic waves: wave vectors; electric and magnetic amplitudes; wave impedance; wave energy; linear, circular and elliptic polarizations; birefringerance and polarization rotation (briefly).

March 12 (Tuesday):

Geometric laws for general waves (my notes): law of reflection and Snell's law of refraction; total internal reflection and evanescent waves.
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 14 (Thursday):

Symmetries of mechanics and electromagnetism (my notes): 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 (my notes): chirality and birefringence; polarization rotation; Faraday affect; Faraday effect in plasma; ionosphere example.

March 19 and March 21:

Spring break, no lectures.

March 26 (Tuesday):

Antennas and radiation: radiation by harmonic currents; near, intermediate, and far zones; spherical waves; multipole expansion; the leading term and the electric dipole moment.

Extra lecture on March 27 (Wednesday):

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

March 28 (Thursday):

Electric dipole approximation: E and H fields in the far zone; the radiated power and its direction dependence; dipole antenna example; rotating dipoles; radiation by Rutherford's classical atom.
Gave out the midterm exam.

April 2 (Tuesday):

EM radiation by atoms and nuclei: classical vs quantum radiation in the electric dipole approximation; selection rules for the electric dipole radiation; forbidden transitions and higher multipoles; selection rules for γ radiation in nuclei.
Magnetic dipole and electric quadrupole radiation (my notes): derivation, fields, net power, angular dependence.

April 4 (Thursday):

Radiation by a center-fed long linear antenna (my notes): general rules; standing current wave I(z); integral for the EM radiation and its direction dependence; examples of direction dependence for L/λ=½,1,2,3,4,6,10; general patterns; net radiation power and the input impedance; antenna as a boundary problem.
Collected the midterm exams.

April 9 (Tuesday):

Introduction to scattering of EM waves: induced dipoles and scattered waves; polarized and un-polarized cross-sections.
Free electron example: polarized cross-sections; unpolarized and net cross-section; polarization by scattering.
Example of a small dielectric sphere: σ∝k⁴; angle and polarization dependence.

April 11 (Thursday):

Multiple scatterers of EM waves: interference and the form factor; Rayleight scattering by gases; attenuation by scattering; Bragg scattering of X rays by crystals.

April 16 (Tuesday):

Origins of special relativity: Galilean relativity and its inconsistency with Maxwell equations; aether theory; Fizeau experiment; aether wind and stellar aberrations; Michelson–Morley experiment; ballistic theory; Fitzgerald–Lorentz contraction and time dilation; Einstein's postulates and their consequences.

Extra Lecture on April 17 (Wednesday):

Superconductivity: forces on magnetic vortices and the critical current; Abrikosov lattices and flux pinning; trouble with high T_c superconductors.
Josephson junctions: tunneling of Cooper pairs; I=I₀×sin(Δφ); voltage and oscillations.

April 18 (Thursday):

Lorentz transforms and spacetime geometry (my notes): Lorentz transforms of spacetime coordinates; relativistic velocity addition; Minkowski spacetime; intervals and lightcones; relativity of past and future; relativistic causality; proper time.
Began 4–vectors (my notes): 4–vector notations and index rules; metric tensor and scalar product.

April 23 (Tuesday):

4–vectors (my notes): O(3,1) group of boosts and rotations; derivative 4–vector; D'Alembert operator and the wave equation.
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.

Extra Lecture on April 24 (Wednesday):

Superconductivity: SQUID magnetometers.
Electric-magnetic duality: magnetic charges and currents; EM symmetry of Maxwell eqs., etc.; charge quantization breaks EM symmetry.

April 25 (Thursday):

Electrodynamics in a manifestly relativistic form (my notes): 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.

April 30 (Tuesday):

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 kinematics of collisions.

May 2 (Thursday):

Action formalism for a relativistic particle (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; 3D formulae for the radiated fields.

May 7 (Tuesday):

Radiation by moving charges (my notes): Larmor formula and its relativistic generalization; synchrotron radiation; linacs v. synchrotrons; angular distribution of radiation.

May 9 (Thursday):

Radiative backreaction: force on the radiating charge; slowdown due to loss of energy; charged particle in a magnetic field.
Frequency of synchrotron radiation: very brief radiation pulses; ω_peak∼γ³×Ω; electron synchrotrons as X-ray sources; wigglers and undulators.
Gave out the final exam.