CLASSICAL ELECTRODYNAMICS (I)

This page logs lectures of the *Classical Electrosynamics (I)*
course (PHY 352 K) taught by
Professor
Vadim Kaplunovsky in Fall 2018 (unique #56195).

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.

- August 30 (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). - September 4 (Tuesday):
- Finish fields of continuous charges (§2.1).

Electric field lines.

Gauss Law and its applicatios (§2.2). - September 6 (Thursday):
- Applications of the Gauss Law (§2.2 and my notes).

Vector derivatives of fields: the gradient, the divergence, and the curl; examples; chain rules; Leibniz rules;**curl(grad)=0**and**div(curl)**=0;~~the Laplacian operator~~. - September 11 (Tuesday):
- Vector calculus and its applications to electrostatics
(§1.3, §2.2–3, and my notes):
Laplace operator; 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.

Dirac's delta-function (§1.5) - September 13 (Thursday):
- 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; continuity of the E
_{∥}; discontinuity of the E_{⊥}; examples; continuous potential across the surface.

Conductors in electrostatics (§2.5). - September 18 (Tuesday):
- Conductors and cavities (§2.5):
Induced charges in conductors; cavities; Faraday cages;
rule of independent surfaces.

Forces on conductors; the electrostatic pressure. - September 20 (Thursday):
- Electrostatic energy (§2.4):
Potential energy of several point charges;
continuous charges and self-interaction;
electrostatic energy as a volume integral of
**E**^{2}. - September 25 (Tuesday):
- Capacitors (§2.5):
Capacitance; parallel plate capacitor; other capacitor types; use of capacitors; energy stored in a capacitor.

Laplace equation for the electric potential (§3.1 and my notes): Laplace equations in one, two, and three dimensions; Earnshaw theorem; mean-value theorem for the potential. - September 27 (Thursday):
- Electrostatic uniqueness theorems (§3.1 and my notes).

Image charges (§3.2): image in a conducting plane; surface charges; force on the original charge. - October 2 (Tuesday):
- Finish image charges (§3.2).

The separation of variables method (§3.3): general approach; 2D example (the slot); equations for the g(y) and for the f(x); series of solutions; fitting to the boundary condition. - October 4 (Thursday):
- Separation of variables method (§3.3 and my notes): 2D box example; 3D square pipe example; separation of variables in polar coordinates (2D)..
- October 9 (Tuesday):
- First mid-term exam.
- October 11 (Thursday):
- Separation of variables in spherical coordinates (§3.3 and my notes):
separating
*r*from θ; Legendre equation and legendre polynomials; series for the inside and the outside of a sphere; charges on the sphere's surface; conducting sphere in external electric field; potentials without axial symmetry and spherical harmonics.

Begin electric dipoles (§3.4.1). - October 16 (Tuesday):
- Electric multipoles and multipole expansion (§3.4 and my notes): dipole moment; quadrupoles and quadrupole moment; higher multipoles; expanding the Coulomb potential into powers of 1/distance; multipole moments and their tensor structure; spherical harmonic expansion; multipole moments of axially symmetric charges.
- October 18 (Thursday):
- Finish multipole expansion (§3.4 and my notes).

Electric dipoles (§3.4.4, §4.1.3, and my notes): Electric field of a dipole; force and torque on a dipole in an external field.

Polarizability and polarization in dielectrics (§4.1): Polarizability of atoms and non-polar molecules; dipole alignment in polar molecules; polarization in dielectric gases and liquids; polarization in crystals. - October 23 (Tuesday):
- Microscopic and macroscopic fields; polarization as a macroscopic field
**P**(**r**).

Bound charges in polarized dielectrics (§4.2 and my notes): Origin of the bound charges; potential due to polarization; surface and volume bound charges; examples.

Dielectrics (§4.2–4 and my notes): The electric displacement**D**=ε_{0}**E**+**P**, and the Gauss Law; the boundary conditions for the**E**and**D**fields (§4.3).

Began Intro to linear dielectrics (§4.4): the succeptibility and the dielectric constant; Coulomb forces in dielectrics. - October 25 (Thursday):
- Intro to linear dielectrics (§4.4 and my notes):
Coulomb forces in dielectrics; surface charges; capacitors.

Boundary problems in linear dielectrics (§4.4.2 and my notes): dielectric ball in external electric field; image charge in a dielectric mirror. - October 30 (Tuesday):
- MKSA vs. Gauss units for dielectrics (my notes).

Electric energy in dielectrics (§4.4.3–4): energy and work in capacitors; force on a dielectric; energy of the electric field in a dielectric.

Intro to magnetic forces and fields (§5.1.1–2): Magnetic forces and their weird directions; magnetic fields lines (my notes); Lorentz force on a charged particle; examples of magnetic fields (my notes). - November 1 (Thursday):
- Magnetic forces (§5.1.2):
particle motion in a magnetic field; magnetic forces on wires;
~~work of magnetic forces~~.

Biot–Savart–Laplace Law (§5.2 and my notes): magnetic field of a long straight wire; Biot–Savart–Laplace formula for general wire geometry. - November 6 (Tuesday):
- Biot–Savart–Laplace Law for the magnetic field of a wire (§5.2 and my notes), general formula and examples: Long straight wire, circular ring, segments, polygons, circular arcs; Biot–Savart–Laplace formula for volume and surface currents; flat current sheet example.
- November 8 (Thursday):
- Continuity equation and steady currents (§5.1.3 and §5.2.1).

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

Symmetries: translations, rotations and reflections; polar nd axial vectors.

Applications of Ampere's Law (§5.3 and my notes): long thin wire, thick wire, flat current sheet,~~solenoid, and toroid~~. - November 13 (Tuesday):
- Applications of Ampere's Law (§5.3 and my notes):
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; rotating charged sphere example; current sheet example. - November 15 (Thursday):
- 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).

Introduction to Magnetic materials (§6.1): diamagnetism, paramagnetism, ferromagnetism, and their origins.

- November 20 (Tuesday):
- Second mid-term exam.
- November 27 (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.

Maybe ferromagnetic materials (§6.4, wikipedia article, hyperphysics article): domains and their behavior; saturation; hysteresis; Curie point. - November 28 (Wednesday) [extra lecture]:
- 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).

Magnetic monopoles and Dirac's charge quantization condition (my notes). - November 29 (Thursday)
- Work of magnetic forces; electric motors and generators.

Electric power, Joule heat, and EMF (electromotive force) (§7.1.2).

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; the induced electric field; calculating the induced**E**fields. - December 4 (Tuesday):
- Time-dependent potentials
*V*(*x,y,x;t*) and**A**(*x,y,x;t*), and gauge transforms (my notes).

Inductance and magnetic energy (§7.2.3–4 and my notes): self-inductance; RL circuit; calculating L; mutual inductance; transformers; energy stored in an inductor; energy of the magnetic field. - December 6 (Thursday):
- LC resonator.

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. - Plan for December 18 (Tuesday) [9 to 12 AM]:
- Final exam.

Last Modified: December 6, 2018. Vadim Kaplunovsky

vadim@physics.utexas.edu