CLASSICAL ELECTRODYNAMICS (I)

This page logs lectures of the *Classical Electrosynamics (I)*
course (PHY 352 K) taught by
Professor
Vadim Kaplunovsky in Spring 2024 (unique 56055).

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.

- January 16 (Tuesday):
- Canceled
- January 18 (Thursday):
- Class organisation & syllabus.

Units in electicity and magnetism: MKSA (SI), Gaussian CGS, and others.

Coulomb law and the electric field; fields of continuous charges (§2.1). - January 23 (Tuesday):
- Finish fields of continuous charges (§2.1).

Electric field lines.

Gauss Law: (§2.2) vector infinitesimal area; flux of a vector field through a surface; Gauss Law.

Applications of the Gauss Law: calculating**E**using symmetries and Gauss Law; examples with spherical symmetry; cylindrical symmetry. - January 25 (Thursday):
- Finish applications of the Gauss Law (§2.2 and my notes):
examples with cylindrical symmetry; examples with planar symmetry.

Vector derivatives of fields: ∇ operator; the gradient, the divergence, and the curl; examples; chain rules; Leibniz rules;**curl(grad)=0**and**div(curl)**=0; the Laplacian operator. - Makeup lecture on January 26 (Friday):
- Vector calculus and its applications to electrostatics
(§1.3, §2.2–3, and my notes):
line, surface, and volume integrals; fundamental theorem for the integrals;
∇×
**E**=0 and the electric potential;**E**=−∇V; Coulomb potential of point-like and continuous charges; examples; Gauss Law in the differential form; Poisson equation for the potential. - January 30 (Tuesday):
- Dirac's delta-function (§1.5).

Point charges and surface charges (§1.5 and §2.3.5): delta functions in 3D; point charges and divergences of their Coulomb fields; surface charges and finite but discontinuous electric field; continuous potential across the surface charge. continuity of the tangent**E**; discontinuity of the normal**E**; examples; continuous potential across the surface. - February 1 (Thursday):
- Surface charges in general (§2.3.5):
continuous potential, continuous
**E**^{tangent}, but discontinuous**E**^{normal}.

Conductors in electrostatics (§2.5.1–2): general rules for conductors; induced charges on conductor surfaces; cavities; Faraday cages;~~rule of independent surfaces~~.

- February 6 (Tuesday):
- Conductors in electrostatics (§2.5.1–3):
cavities and the rule of independent surfaces;
forces on conductors and the electrostatic pressure.

Electrostatic energy (§2.4): Potential energy of several point charges. - February 8 (Thursday):
- Electrostatic energy (§2.4):
electrostatic energy of continuous charges;
electrostatic energy as a volume integral of
**E**^{2}; interactions versus self-interactions for discrete charges.

Capacitors (§2.5): capacitance; energy stored in a capacitor. - February 13 (Tuesday):
- Capacitors (§2.5): uses of capacitors; C of a parallel plate capacitor;
other types of capacitors.

Laplace equation for the electric potential (§3.1 and my notes): Laplace equations in one, two, and three dimensions; soap film as a 2D example; Earnshaw theorem; mean-value theorem. - February 15 (Thursday):
- Electrostatic theorems (§3.1 and my notes):
electrostatic uniqueness theorems.

Image charges (§3.2): image in a conducting plane; surface charges. - February 20 (Tuesday):
- Finished image charges:
forces, work, and energy for the imaged charges.

Separation of variables method (§3.3 and my notes): general approach; 2D infinite slot model; equations and boundary conditions for the*f(x)*and the*g(y)*; series of solutions; fitting to the boundary potential; examples; a finite-depth slot. - February 22 (Thursday):
- Separation of variables method (§3.3 and my notes):

Cartesian coordinates in 2D: repeated the finite-depth slot example.

Cartesian coordinates in 3D: a half-infinite rectangular pipe.

Polar coordinates in 2D: equations and boundary conditions for a cylindrical cavity; solving the equations; general solution for a general boundary potential; the square wave example;~~space outside a cylinder~~.

Begin spherical coordinates in 3D for potentials with axial symmetry: separating*r*from θ; Legendre equation and legendre polynomials; Maybe potentials without axial symmetry and spherical harmonics. - February 27 (Tuesday):
- First midterm test.
- February 29 (Thursday):
- Separation of variables method (§3.3 and my notes):

Finished polar coordinates in 2D: space outside a cylinder.

Spherical coordinates in 3D for potentials with axial symmetry: solutions for the inside and the outside of a sphere; charges on the sphere's surface; conducting sphere in external electric field.

Spherical coordinates in 3D for potentials without axial symmetry: overview of spherical harmonics;~~separation of variablles and radial dependence; general 3D solutions~~. - March 5 (Tuesday):
- Midterm results.

Finished separation-of-variables in spherical coordinates: spherical harmonics and radial dependence; general 3D solutions.

Electric dipoles (§3.4, §4.1, and my notes): a simple dipole and its potential; dipole moment of s system of charges; electric field of a dipole; force and torque on a dipole in an external field; potential energy of a dipole. - March 7 (Thursday):
- Finished potential energy of a dipole
and its relation to the torque and the force (my notes).

Multipole expansion (§3.4 and my notes): expanding the Coulomb potential into powers of 1/distance; quadrupole moment and quadrupole examples; octupole moment and examples; higher multipoles; multipole moments and their tensor structure; spherical harmonic expansion; multipole moments of axially symmetric charges. - March 12 and 14:
- Spring Break, no classes.
- March 19 (Tuesday):
- Polarization of dielectrics (§4.1 and my notes):
Microscopic dipole moments and macroscopic polarization;
induced dipoles in atoms and molectules; alignment of polar molecules;
polarization in condensed matter.

Bound charges (§4.2–3 and my notes): Origin of the bound charges; potential due to polarization; surface and volume bound charges; examples; electric displacement field**D**; Gauss law for**D**; boundary rules for the**E**and**D**field.

Intro to linear dielectrics (§4.4.1 and my notes): the succeptibility and the dielectric constant; Coulomb forces in dielectrics; surface charges; capacitors.

- March 21 (Thursday):
- Boundary problems in linear dielectrics (§4.4.2 and my notes):
dielectric ball in external electric field; image in a dielectric slab.

Capacitor energy and force (§4.4.4): capacitor energy; electric and mechanical work on a capacitor; force on a dielectric.

Started electrostatic energy in dielectrics (§4.4.3). - March 26 (Tuesday):
- Electrostatic energy in dielectrics (§4.4.3).

MKSA vs. Gauss units for dielectrics (my notes).

Intro to magnetic forces and fields (§5.1): Magnetic forces and their weird directions; magnetic fields lines (my notes); examples of magnetic fields (my notes); Lorentz force on a charged particle; particle motion in a magnetic field. - March 28 (Thursday):
- Magnetic forces on currents (§5.1.3).

Biot–Savart–Laplace Law (§5.2.2 and my notes): magnetic field of a long straight wire; Biot–Savart–Laplace formula for general wire geometry; Examples: long straight wire, circular ring, segments, polygons, circular arc.

Biot–Savart–Laplace Law (§5.2.2 and my notes): formulae for volume and surface currents; flat current sheet example. - April 2 (Tuesday):
- Finish flat current sheet example (my notes, pages 18–19):
discontinuity of the magnetic field.

Continuity equation and steady currents (§5.2.1 and my notes).

Divergence and curl of the magnetic field; Ampere's Law (§5.3.1–2 and my notes).

Symmetries: translations and rotations; mirror reflections; polar and axial vectors; examples. - April 4 (Thursday):
- Applications of Ampere Law (§5.3 and my notes):
long thin wire, thick wire, flat current sheet, solenoid and toroid.

Vector potential for the magnetic field (§5.4.1–2 and my notes):**B**=∇×**A**; gauge transforms; magnetic flux; equations for the vector potential; current sheet example. - April 9 (Tuesday):
- Vector potential for the magnetic field (§5.4.1–2 and my notes):
rotating charged sphere example.

Multipole expansion for magnetic fields (§5.4.3 and my notes): the expansion; explicit formlae for the dipole terms and dipole moments. Forces and torques on magnetic dipoles (§6.1.2 my notes).

Magnetic moments of atoms. - April 11 (Thursday):
- Second midterm test..
- Extra lecture on April 12 (Friday):
- 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.

Aharonov–Bohm effect (my notes): setup; separate gauges for two electron paths; gauge dependence of the propagation amplitude; interference Δφ depends on magnetic flux*between*the two electon paths; quantum units of the magnetic flux.

Superconducting QUantum Interferomerty Devices (my notes): overview of superconfuctivity and Josephson junctions (very brief); net supercurrent through a SQUID; Aharonov–Bohm-like phases and interference in a SQUID; SQUIDs as sensitive magnetometers. - April 16 (Tuesday):
- Magnetization and bound currents (§6.2 and my notes):
explanation, examples, and physical origins of bound currents.

The H field (§6.3 and my notes): the equations and the pitfalls; boundary conditions for the**B**and**H**magnetic fields; the electric-magnetic analogy.

Linear magnetic materials (§6.4 and my notes): succeptibility and permeability; electromagnets. - April 18 (Thursday):
- Ferromagnetic materials (briefly)
(§6.4, Dr. Rudolf Winter's web page):
domains and their behavior; saturation; hysteresis; Curie point.

EMF (electromotive force) and generators (§7.1.2): batteries and generators; EMF and voltage; work of magnetic forces; electric motors and generators.

Motional EMF and Faraday's Law (§7.1.3, §7.2.1–2 and my notes): EMF in a moving wire; relation to the magnetic flux; Faraday's Law of Induction; Lenz rule. - Plan for April 23 (Tuesday):
- Faraday's Law of Induction (§7.2.2 and my notes):
the induced electric field;
calculating the induced
**E**fields; time-dependent potentials V(*x,y,x;t*) and**A**(*x,y,x;t*); gauge transforms.

Self-inductance and mutual inductance (§7.2.3 and my notes): self-inductance; RL circuit; calculating L; mutual inductance; transformers; maybe energy stored in an inductor; energy of the magnetic field. - Tentative plan for April 25 (Thursday):
- Magnetic energy (§7.2.4 and my notes):
Inductor energy; energy of the magnetic field; example.

Maxwell's displacement current and the Maxwell–Ampere equation (§7.3.1–2 and my notes).

Maxwell equations (§7.3.3–6 and my notes): full set of Maxwell equations; macroscopic Maxwell equations in matter; boundary conditions; electromagnetic waves. - Tentative plan for the extra lecture on April 26 (Friday):
- Electric–magnetic duality and Dirac monopoles (my notes): Electric–magnetic duality in vacuum; magentic charges and currents; monopoles in quantum mechanics and the trouble with the vector potential; Dirac's 2-potential solution; Dirac's charge quantization rule; implications for QED and other quantum field theories; dyons and their angular momenta.

Last Modified: April 18, 2024. Vadim Kaplunovsky

vadim@physics.utexas.edu