Electromagnetic Theory: Lecture Log

January 19 (Wednesday):
Syllabus and admin: course content, textbook, prerequisites, homework, exams, grades, etc. (see the main web page for the class).
Laplace or Poisson equations for the Φ(x): boundary conditions; methods of solving (outline); image charges.
January 21 (Friday):
Separation of variables: outline of the method; spherical shell example; using spherical harmonics.
Green's functions: inverse operators; Dirichlet and Neumann boundary conditions; using Green's functions.
Regular lecture on January 24 (Monday):
Green's functions and their uses: symmetry; Green theorem (for non-trivial bounday potentials or fields); half-space example.
Likbez lecture on January 24 (Monday):
Separation of variables in 2D: Solving Laplace equation for Φ(x,y)=A(x)B(y); general solution as an infinite series; finding the coefficients; examples.
Separation of variables in 3D (Cartesian coordinates).
Separation of variables in spherical coordinates.
January 26 (Wednesday):
Electric multipole expansion: potentials of compact charged bodies; expanding 1/|x−y|; Legendre polynomials; spherical harmonics, spherical multipole moments, and their potentials; dipole moment in detail.
January 28 (Friday):
Finished electric multipole expansion: quadrupole term; quadrupole moment tensor in detail; examples; octupole terms and octupole tensor; higher multipoles.
January 31 (Monday):
Steady currents: continuity equation and local charge conservation; divergenceless steady currents; Kirchhoff Law.
Introduction to magnetostatics: 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.
February 2 (Wednesday):
Highlights of magnetostatics: vector potential A(x) and equations it obeys; examples of calculating A(x) and B(x); multipole expansion; magnetic dipole moment in detail.
February 4 (Friday):
Canceled due to bad weather.
Regular lecture on February 7 (Monday):
Magnetic dipoles: multipole expansion for the volume current; magnetic dipole moment in detail; gyromagnetic ratio; fields of point dipoles (electic and magnetic); forces and torques on dipoles; magnetic effects on atoms.
Make-up lecture on February 7 (Monday):
Finished magnetic dipoles.
Polarization and Magnetization: macroscopic fields; polarization and magnetization; bound charges in a dielectric; electric dicplacement field D; dielectric constant; bound currents in magentic materials; B and H magnetic fields; magnetic equation of state; boundary conditions in dielectrics and magnets.
February 9 (Wednesday):
Polarization and Magnetization: dielectric sphere example; scalar magnetic potential Ψ; permanent magnet examples; multivalued Ψ(x) in presence of wires.
February 11 (Friday):
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; started forces on dielectrics in electric fields.
Regular lecture on February 14 (Monday):
Finished electrostatic energy: forces on dielectrics in electric fields; energy in non-linear dielectrics; hysteresis and energy loss (briefly).
Started Faraday Induction Law: Faraday's flux rule; motional EMF, and its relation to the flux rule.
Extra lecture on February 14 (Monday):
Classical and quantum mechanics of a charged particle: Classical Lagrangian and equations of motion; classical Hamiltonian; quantum Hamiltonian; gauge transforms and their effects of the wave function; generalization to the quantum field theory.
February 16 (Wednesday):
Finished Faraday Induction Law: induced non-potential electric field; ∇×E=−∂B/∂t; scalar and vector potentials for time-dependent fields; gauge transforms and gauge-fixing.
Magnetic energy: energy of inductor coil; energy of magnetic field; energy loss to hysteresis; forces on magnetic materials.
February 18 (Friday):
Complex amplitudes and impedance.
Mutual inductance and transformers (briefly).
February 21 (Monday):
Eddy currents and skin effect: demo#1; demo#2; diffusion equation for the current and the magnetic field; solving the diffusion equation: how the field penetrates a conductor; skin effect for AC currents.
February 23 (Wednesday):
Maxwell equations: the displacement current; Maxwell equations and electromagnetic waves; equations for the potentials A and Φ; transverse gauge gauge; Landau gauge.
February 25 (Friday):
Green's functions of the d'Alembert operator: Fourier transformed Green's functions; causality; retarded and advanced Green's functions; retarded potentials 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.
Regular lecture on February 28 (Monday):
Stress tensor: pressure and stress forces in continuous media; stress tensor; Tij=Tji; stress tensor and momentum flow; local conservation of momentum.
Electromagnetic momentum: EM force density, momemntum density, and Maxwell's stress tensor; proof of local momentum conservation; tension and compression of magnetic fields; pressure of thermal EM radiation.
Began plane EM waves: wave vectors; electric and magnetic amplitudes.
Extra lecture on February 28 (Monday):
Electric–Magnetic duality and Dirac Monopoles: duality of EM fields; duality of charges and currents; magnetic monopoles and troubles with their vector potentials; Dirac monopoles and charge quantization; electric-magnetic duality in QFT; angular momentum of a dyon.
March 2 (Wednesday):
Plane electromagnetic waves: electric and magnetic amplitudes; wave impedance; wave energy; linear, circular and elliptic polarizations.
March 4 (Friday):
Geometric laws for general waves: law of reflection and Snell's law of refraction; total internal reflection and evanescent waves.
Reflection and refraction of electromagnetic waves: 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.
Regular lecture on March 7 (Monday):
Finish Reflection and refraction of EM waves: phase shift in total internal reflection.
Dispersion and attenuation of EM waves: 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.
Extra lecture on March 7 (Monday):
Superfluids: Bose–Einstein condensation and the condensate field; density and velocity of the superfluid.
Superconductivity: Cooper pairs and their condensation; charged superfluid; Meissner effect.
March 9 (Wednesday):
Gaussian wave packets.
Microscopic origin of dispersion: single-resonance toy model; multi-resonance model; normal and anomalous dispersion; low frequency behavior α(ω); Drude conductivity in metals.
March 11 (Friday):
Microscopic origin of dispersion, high-frequencyα(ω): plasmas 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; dispersion and spreading out of wave packets; signal rate.
March 14, 16, and 18:
Spring break.
March 21 (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; Faraday effect in plasma.
March 23 (Wednesday):
March 25 (Friday):
Faraday effect in plasma.
Introduction to waveguides: Maxwell equations and boundary conditions; dispersion relations and cutoff frequencies; TEM waves.
Regular lecture on March 28 (Monday):
Waveguides: TEM waves; TE waves; TM waves; wave power; speed of wave energy in a waveguide; waves in a rectangular waveguides.
Make-up lecture on March 28 (Monday):
More waveguides: waves in a circular waveguide; effects of wall resistivity on the boundary conditions; wave attenuation due to wall resistivity; frequency dependence of the attenuation rate.
March 30 (Wednesday):
Microwave cavities: TM and TE standing waves; modes and resonant frequencies of a rectangular cavity; modes and frequencies of a cylindrical cavity.
Quality factor of a resonator: mechanical example; resonance width; LRC circuit example.
Quality of a microwave cavity: general estimate; example of a geometric factor.
April 1 (Friday):
Finished Microwave cavities: example of a geometric factor.
Optic fibers as waveguides: overview; fiber types; multiple rays for step-index fibers; signal spread; geometric optics for smooth-index fibers.
Regular lecture on April 4 (Monday):
Finished optic fibers: wave optics for smooth-index fibers; mode counting; wave equations for single-mode fibers.
Extra lecture on April 4 (Monday):
Superconductivity: flux quantization; magnetic vortices; type II and type II superconductors.
April 6 (Wednesday):
Radiation by compact antennas: radiation by harmonic currents; near, intermediate, and far zones; spherical waves; multipole expansion; the leading term and the electric dipole moment; the basics of electric dipole radiation.
April 8 (Friday):
Electric dipole radiation: linear antenna example;non-linear dipoles; Rutherford atom example.
Higher multipoles: first subleading order; magnetic dipole radiation; begin electric quadrupole radiation.
April 11 (Monday):
Finish Radiation by compact antennas: electric quadrupole radiation; higher miltipoles.
Quantum radiation of photons: quantum transitions; Fermi's Golden rule; intro to quantum EM fields and photons; photon emission by excited atoms in the dipole approximation; quantum-classical correspondence.
April 13 (Wednesday):
Quantum radiation of photons: classical amplitudes as limits of quantum matrix elements; allowed and forbiddent transitions in atoms; selection rules for the allowed transitions.
April 15 (Friday):
Gamma decays and selection rules in nuclear physics.
Scalar spherical waves in detail: separation of variables; spherical Bessel functions j and n; small-raius and large-radius asymptotics; divergent spherical waves and the Hankel functions h.
Maybe begin spherical EM waves: coordinating the components Ei(x) and Hi(x); TM waves and TE waves.
Regular lecture on April 18 (Monday):
Spherical EM waves: coordinating the component waves Ei(x) and Hi(x); TM waves and TE waves; no ℓ=0 modes of EM waves.
Extra lecture on April 18 (Monday):
Josephson junctions: tunneling of Cooper pairs; I=I0×sin(Δφ); voltage and oscillations.
April 20 (Wednesday):
Spherical EM waves: long-distance and short-distance limits; electric multipoles source TM waves, magnetic multipoles source TE waves; power and its angular distribution for the waves with specific ℓ and m.
Maybe begin: radiation by a long antenna.
April 22 (Friday):
Radiation by a long antenna: center-fed long linear antenna; 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.
April 25 (Monday):
Receiving antennas: reciprocity theorem; directionality and gain; effective aperture; short dipole example; impedance matching; general antennas.
Introduction to scattering: induced multipoles and re-radiation; partial and total cross-sections; polarized cross-sections; begin example of a small dielectric sphere.
April 27 (Wednesday):
Scattering examples: small dielectric sphere: σ∝k4, angular dependence, and polarization; Thomson scattering by a free electron.
Started multiple scatterers.
April 29 (Friday):
Multiple scatterers of EM waves: interference and the form factor; Rayleight scattering by gases; attenuation by scattering; Bragg scattering by crystals.
Regular lecture on May 2 (Monday):
Partial wave analysis (for the scalar waves): partial waves; radial waves and sphase shifts; scattering amplitude and total cross-section in terms of phase shifts; scattering off a hard sphere; small sphere limit; large sphere limit.
Extra lecture on May 2 (Monday):
Aharonov–Bohm effect: role of the vector potential; gauge transforms of wave functions and of propagation amplitudes; interference and the Aharonov–Bohm effect; cohomology of magentic fluxes.
SQUID magnetometers: intro to the Superconducting Quantum Interferometry Devices; currents through two Josephson junctions; phase analysis in a magnetic field; maximal current as a function of the magnetic flux.
May 4 (Wednesday):
Diffraction: Introduction; Green's theorem; Kirchhoff approximation; integrals over the aperture(s); Fresnel and Fraunhofer diffraction; Fraunhofer limit in detail; rectangular aperture as an example.
May 6 (Friday):
Diffraction: multiple apertures, interference, and diffraction gratings; diffraction in a circular aperture; Airy disk; laser Moon ranging example; telescopes and resolution.

Last Modified: May 6, 2022.
Vadim Kaplunovsky