- 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=mc*; energy-momentum 4–vector^{2}*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.

Last Modified: May 2, 2018. Vadim Kaplunovsky

vadim@physics.utexas.edu