Lecture Log for PHY 352 L
CLASSICAL ELECTRODYNAMICS (II)

This page logs lectures of the Classical Electrosynamics (II) course (PHY 352 L) taught by Professor Vadim Kaplunovsky in Spring 2026 (unique 59780).

To help the students follow the class, this log lists the subjects covered by each lecture, with references to appropriate textbook chapters and sections, and also external links, if any.

Since the pace of the course will vary depending on how well (or how poorly) the students understand the material, I would not be able to tell in advance which specific subjects I will cover during a particular future lecture. Therefore, at any particular time, this log will be limited to the lectures I have already given, plus one tentative listing of what I plan to say in the very next lecture.

Most lectures should be video recorded and the records available on Canvas. For the few lectures that did not get recorded because of technical glitches, I shall scan the notes I have used in class and links the scans to this page.

Lectures

January 13 (Tuesday):

Syllabus: textbook, notes, and subjects to learn; logistics; homeworks, exams, and grades.
Continuity equations and local conservation laws: Local charge conservation; local energy conservation; EM energy and power; Poynting theorem and Poynting vector for the EM energy flow; examples.
stress tensor and its relation to the momentum flow.

January 15 (Thursday):

Electromagnetic momentum and stress tensor: local momentum conservation; EM momentum density and force density; Maxwell's EM stress tensor; examples.
EM angular momentum: construction and an example; L due to a magnetic monopole.

January 20 (Tuesday):

EM angular momentum around a magnetic monopole.
Magnetic work (Griffith §8.3): Lorentz forces do no work; but macroscopic magnetic forces convert mechanical work↔electric work; quantum effects and permanent magnets.
Complex amplitudes and impedances: complex amplitudes of harmonic variables; impedance; impedances of resistors, inductors, and capacitors; serial and parallel circuits; LC resonant circuit; time-averaged power.

January 22 (Thursday):

Electromagnetic waves 3D wave equation and plane wave solutions; EM wave equation and speed of light; spectrum of EM waves; power and intensity of an EM wave; light pressure. Polarizations of plane EM waves: linear (planar) polarizations; circular polarizations.

January 27 (Tuesday):

Cancelled due to bad weater.

January 29 (Thursday):

Finished Polarizations of plane EM waves: circular polarizations; elliptic polarizations; superpositions of polarized waves; polarization fiters.
Refraction and reflection of general waves: geometric laws of reflection and refraction; total internal reflection.
Refraction and reflection of EM waves, the head-on case: boundary conditions and amplitudes; relection and transmission coefficients; reflectivity and transmissivity; Fresnel equations.
Refraction and reflection of EM waves, intro to the oblique case: boundary conditions and amplitudes; polarization dependence.

February 3 (Tuesday):

Refraction and reflection of EM waves, the oblique case: polarization normal to the plane of incidence: boundary conditions, t and r coefficients, reflectivity and transmissivity; polarization within the plane of incidence: boundary conditions, t and r coefficients, reflectivity and transmissivity, Brewster angle; polarization by reflection; amplitudes for the total internal reflection.
EM waves in conducting materials: Complex effective conductivity, complex ε_eff(ω) and complex refraction index n(ω); attenuating EM waves; poor conductor limit; good conductor limit; skin effect and skin depth; high-frequency impedance of a wire; diffusion equation for the EM fields and the current; demo of eddy currents.

Make-up class on February 4 (Wednesday):

EM waves in conductors: reflection of EM waves off a conductor surface, reflectivity and skin depth; inherently complex ε(ω) and μ(ω); water example; attenuation of EM waves due to dielectric and/or magnetic losses. Absorbtion of EM waves by water.
Math of Gaussian wave packets.
Dispersion of waves: phase and group velocities of waves; plasma example; normal and anomalous dispersion;

February 5 (Thursday):

Dispersion of waves: dispersion of wave packets; maximal signal rate.
Microscopic origin of dispersion: dispersion in plasma; single-resonance toy model of an atom; multi-resonance model; normal and anomalous dispersion in gases; normal and anomalous dispersion in condenced matter.

February 10 (Tuesday):

Guided waves: Waveguides; 2D Maxwell equations for waveguides; modes and cutoff frequencies; TEM waves in coaxial waveguides; TE and TM waves in general; TE and TM waves in rectangulr waveguides; round waveguides (briefly); resonant cavities.

February 12 (Thursday):

Electromagnetic potentials: vector and scalar potentials; gauge transforms; Coulomb gauge condition; transverse currents; Landau gauge condition; causality; solving the forced wave equation; retarded potentials of continusous charges and currents; example; Jefimenko equations for the magnetic and the electric fields.

February 17 (Thursday):

Dynamics of a charged particle: classical Lagrangian; Euler–Lagrange equation; classical Hamiltonian and Hamilton equations; quantum momentum operators and Hamilton operator; gauge transforms, local phase transforms, and covariant derivatives; gauge invariance of physical quantities; WKB approximation and the wave-function phases; particles with spin; covariant Dirac equation; discussion of QED and other gauge theories.

February 19 (Thursday):

Midterm exam #1.

February 24 (Tuesday)

EM potentials of continuous charges and currents [repeating second half of 2/12 lecture]: solving the forced wave equation; causality and retarded potentials; example; Jefimenko equations for the magnetic and the electric fields.
Liénard–Wiechert potentials: retarded potentials for a moving point charge; variance of the retarded time and the 1/(1-n·β) factor; potentials of a particle moving at constant velocity; E and B fields of such particle.

Plan for February 26 (Thursday)

E and B fields for Liénard–Wiechert potentials: partial derivatives at observer time versus retarded time; working out the electric field; the generalized Coulomb field and the acceleration field; the generalized Coulomb term in E, the acceleration term in E, working out the magnetic field.
Power radiated by a point charge: radiation comes only from E_accel only; non-relativistic Larmor formula; angular distribution; CRT and Rutherford atom examples; intro to radiation by relativsitic point charges; case of accleration parallel to velocity: the angular distribution and the net power.

Tentative plan for March 3 (Tuesday)

Finish Power radiated by a relativistic point charge: case of acceleration normal to velocity: the angular distribution and the net power; Liénard–Larmor formula for the general case; synchrotron radiation example; linac example.
Radiation by an oscillating dipole: details TBA.