CLASSICAL ELECTRODYNAMICS (I)

This page logs lectures of the *Classical Electrosynamics (I)*
course (PHY 352 K) taught by
Professor
Vadim Kaplunovsky in Fall 2017 (unique #56395).

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 31 (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 5 (Tuesday):
- Finish fields of contnous charges (§2.1).

Electric field lines.

Gauss Law and its applicatios (§2.2). - September 7 (Thursday):
- Finish 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 12 (Tuesday):
- Fundamental theorems and their application to electrostatics
(§1.3, §2.2–3, and my notes):
Line, surface, and volume integrals;
∇×
**E**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 14 (Thursday):
- Delta-functions, 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.

Began conductors in electrostatics (§2.5). - September 19 (Tuesday):
- Conductors and cavities (§2.5):
General rules for conductors; induced charges; cavities Faraday cages;
rule of independent surfaces.

Forces on conductors; the electrostatic pressure. - September 21 (Thursday):
- Electrostatic energy and capacitors (§2.4 and §2.4.5):
Capacitors; energy stored in a capacitor; potential energy of several point charges;
continuous charges and self-interaction; electrostatic energy as a volume integral of
**E**^{2}. - September 26 (Tuesday):
- Finish electrostatic energy (sect;2.4): examples; self-energy vs. interactions.

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 28 (Thursday):
- Electrostatic theorems (§3.1 and my notes):
the uniqueness theorems.

Image charges (§3.2): image in a conducting plane; surface charges; force on the original charge. - October 3 (Tuesday):
- 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; the rectangular pipe example. - October 5 (Thursday):
- Separation of variables method (§3.3 and my notes):
3D rectangular box example; separation in polar coordinates (2D); separation in spherical coordinates (3D);
~~surface charges on the sphere; conducting sphere in external electric field~~. - October 10 (Tuesday):
- First midterm exam
- October 12 (Thursday):
- Separation of variables in spherical coordinates (§3.3 and my notes):
surface charges on the sphere; conducting sphere in external electric field;
spherical harmonics.

Electric multipoles (§3.4.1): electric dipole; dipole moment; quardupole, octupole, and higher multipoles.

Began multipole expansion (§3.4.2 and my notes): Expanding 1/distance; expanding the Coulomb potential into multipole momenta. - October 17 (Tuesday):
- Multipole expansion (§3.4.2–3 and my notes):
Multipole moments and their tensor structure; spherical harmonic expansion;
multipole moments of axially symmetric charges; origin dependence of multipole moments.

~~More 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~~. - October 19 (Thursday):
- 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. Bound charges due to polarization (§4.2): Bound charges in the bulk and on the surface of a dielectric; origin of the bound charges. - October 24 (Tuesday):
- 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).

Linear dielectrics (§4.4): the succeptibility and the dielectric constant; Coulomb forces in dielectrics; capacitors.

Examples of dielectric boundary problems (§4.4.2 and my notes): dielectric ball in external electric field;~~image charge in a dielectric mirror~~. - October 26 (Thursday):
- Finish dielectric boundary problems (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.

MKSA vs. Gauss units for dielectrics (my notes). - October 31 (Tuesday):
- Magnetic forces and electric currents (§5.1): Intro to magnetic forces, magnetic fields, and their weird directions; Lorentz force on a charged particle; cyclotron motion; magnetic forces on electric currents; work of magnetic forces.
- November 2 (Thursday):
- Continuity equation for the electric current
(§5.1.3 and my notes).

Biot–Savart–Laplace Law and examples of its application (§5.2 and my notes): Forces between long parallel wires; Biot–Savart–Laplace formula for general wire geometry; examples:**B**(infinite straight wire),**B**(circular ring), segments, polygons, circular arc,~~current sheet~~. - November 7 (Tuesday):
- Biot–Savart–Laplace formula for volume and surface currents;
flat current sheet example (§5.2 and my notes).

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

Applications of Ampere's Law (§5.3 and my notes): long thin wire, thick wire, flat current sheet. - November 9 (Thursday):
- 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 14 (Tuesday):
- 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 15 (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;
generalization to quantum field theory.

Aharonov–Bohm effect (my notes). - November 16 (Thursday):
- 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**H**and**H**magnetic fields; the electric-magnetic analogy.

Linear magnetic materials (§6.4 and my notes): succeptibility and permeability; electromagnets. - November 21 (Tuesday):
- Second midterm exam
- November 28 (Tuesday):
- Ferromagnetic materials (§6.4,
wikipedia article,
hyperphysics aritice):
domains and their behavior; saturation; hysteresis; curie point.

Ohm's Law (§7.1 and my notes):**J**=σ**E**; Lorentz–Drude explanation of the Ohm's Law; conductors vs semiconductors. vs. insulators; equations and boundary conditions for**E**in conductors; calculating net resistance;~~electric power and Joule heat; the EMF (electromotive «force»)~~. - November 29 (Wednesday) [extra lecture]:
- Magnetic monopoles and the electric charge quantization (my notes):
Dummy magnets, Aharonov–Bohm effect, and charge quantization;
Dirac's vector potentials for a monopole; Dirac charge condition;
modern unified theories.

Superconductivity, monopoles, and QCD (no notes, sorry): Meissner effect; magnetic flux tubes; monopoles imbedded in a superconductor; quark confinement; QCD (quantum chromodynamics) as a gauge theory; chromomagnetic monopoles; chromomagnetic superconductivity as explanation of quark confinement. - November 30 (Thursday):
- Electric power, Joule heat, and EMF (electromotive force).

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.

Time-dependent potentials*V*(*x,y,x;t*) and**A**(*x,y,x;t*), and gauge transforms (my notes). - December 5 (Tuesday):
- Inductance and magnetic energy (§7.2.3–4 and my notes):
mutual inductance; self-inductance; the LR circuit;
energy stored in an inductor; energy of the magnetic field.

Maxwell's displacement current and Maxwell–Ampere equation (§7.3.1–2 and my notes). - December 7 (Thursday):
- Maxwell equations (§7.3.3–6 and my notes):
Full set of Maxwell equations; macroscopic Maxwell equations in matter; boundary conditions;
electromagnetic waves.

Review of midterm problems. - Plan for December 16 (Saturday) [2 to 5 PM]:
- Final Exam.

Last Modified: December 7, 2017. Vadim Kaplunovsky

vadim@physics.utexas.edu