- 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*; stress tensor and momentum flow; local conservation of momentum._{ij}=T_{ji}

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∝*k*^{4}; 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*=*I*_{0}×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=mc*; energy-momentum 4–vector^{2}*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}∼γ^{3}×Ω; electron synchrotrons as X-ray sources; wigglers and undulators.

Gave out the final exam.

Last Modified: May 9, 2019. Vadim Kaplunovsky

vadim@physics.utexas.edu