CLASSICAL ELECTRODYNAMICS (I)

This page logs lectures of the *Classical Electrosynamics (I)*
course (PHY 316) taught by
Professor
Vadim Kaplunovsky in Spring 2016 (unique #55930).

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.

- January 19 (Tuesday):
- 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 21 (Thursday):
- Electric field lines; Gauss Law and its applications (§2.2).

Math of scalar and vector fields (§1.2–3): partial derivatives; gradient; the ∇ operator; scalar and vector fields and how they transform under rotations. - January 26 (Tuesday):
- Gradient, divergence, and curl (§1.2 and my notes):
Divergence and curl of a vector field; examples; chain rules; Leibniz rules;
**curl(grad)=0**and**div(curl)=0**; the Laplacian operator. - January 28 (Thursday):
- 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. - February 2 (Tuesday):
- Delta-functions, point charges, and surface charges (§1.5 and §2.3.5):
math and physics of δ(x-x
_{0}); delta functions in 3D; point charges and divergences of their Coulomb fields; surface charges; continuity of the**E**_{∥}; discontinuity of the**E**_{⊥}; example; continuous potential across the surface.

- February 4 (Thursday):
- Conductors in electrostatics (§2.5):
general rules; induced charges; forces on conductors; capacitors and capacitance.

- February 9 (Tuesday):
- Electrostatic work and energy (§2.4):
Energy stored in a capacitor; potential energy (U) of a probe charge;
U of several point charges; continuous charges and self-interaction;
electrostatic energy as a volume integral of
**E**^{2}. - February 11 (Thursday):
- Energy of the electric field (§2.4).

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; boundary conditions and the uniqueness theorem. - February 16 (Tuesday):
- Electrostatic theorems: finish the uniqueness theorem; the second uniqueness theorem.

Image charges (§3.2): image in a conducting plane; surface charges; force on the original charge. - February 18 (Thursday):
- Image charges (§3.2): image in a conducting sphere; un-grounded spheres; other kinds of images.

Variable separation method (§3.3): general approach; 2D example; equations for the*f(x)*and*g(y)*; solving the equations; series for the*V(x,y)*. - February 23 (Tuesday):
- Separation of variable (§3.3 and my notes):
Finish the 2D box example; separation of polar coordinates; separation of spherical coordinates;
~~surface charges on a sphere; metal sphere in the external field.~~ - February 25 (Thursday):
- Separation of variables for the sphere (§3.3 and my notes):
Clarify expansion into Legendre polynomials; surface charges on the sphere;
conducting sphere in external electric field.

Multipole expansion (§3.4): Potentials of the electric dipole, quadrupole, octupole,*etc.*; multipole expansion of the Coulomb potential.

- March 1 (Tuesday):
- Multipole expansion (§3.4 and my notes):
Multipole expansion of the Coulomb potential; radial depemdence of the multipoles;
angular dependence and tensor structures of the multipole moments;
moments of axially symmetric charges;
coordinate dependence of multipole moments.

Electric dipoles (§3.4.4, §4.1.3, and my notes): Electric field of a pure dipole; force, torque, and potential energy of a dipole in an external electric field. - March 3 (Thursday):
- First midterm exam.
- March 8 (Tuesday):
- Polarization of a dielectric (§4.1):
induced dipole moments in atoms and non-polar molecules;
preferencal alignment of polar molecules; macroscopic polarization field
**P**; linear and non-linear dielectrics.

Bound charges on the surface and in the volume of a dielectric (§4.2). - March 10 (Thursday):
- 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~~. - March 15 and March 17:
- Spring break.
- March 22 (Tuesday):
- Dielectric boundary problems:
image charge in a dielectric mirror (§4.4.2 and my notes).

Electric energy in dielectrics (§4.4.3–4): dielectrics in capacitors; energy and work in capacitors; force on a dielectric; energy of the electric field in a dielectric. - March 24 (Thursday):
- Finish dielectrics: MKSA vs. Gauss units (my notes).

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 and current densities. - March 29 (Tuesday):
- Work of magnetic forces (§5.1.2–3).

Continuity equation for the electric current (§5.1.3).

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) - March 31 (Thursday):
- Examples of Biot–Savart–Laplace Law
(§5.2 and my notes):
circular ring; segments; polygons; circular arc; current sheet.

Curl and divergence of the magnetic field; Ampere's Law (§5.3.1–2 and my notes) - April 5 (Tuesday):
- Applications of the Amperes' Law (§5.3.3 and my notes).

Vector potential for the magnetic field (§5.4.1):**B**=∇×**A**; gauge transorms; Lagrangian and Hamiltonian for a charged particle; magnetic flux.

Equations for the vector potential (§5.4.1–2 and my notes). - April 7 (Thursday):
- Equations for the vector potential (§5.4.1–2 and my notes):
Charged sphere example; boundary conditions for current sheets.

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). - April 12 (Tuesday):
- Magnetic materials (§6.1):
diamagnetism, paramagnetism, and ferromagnetism;
origin of paramagnetism; origin of diamagnetism; how to tell diamagnetic materials from paramagnetic;
origin of ferromagnetism; domains.

Magnetization**M**and bound currents (§6.2). - April 14 (Thursday):
- The bound currents (§6.2): the explanation; example of usage.

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

Linear magnetic materials (§6.4): succeptibility and permeability; electromagnets. - April 19 (Tuesday):
- Ferromagnetic materials (§6.4): domains and their behavior; saturation;
hysteresis; curie point.

Ohm's Law (§7.1):**J**=σ**E**; Lorentz–Drude explanation of the Ohm's Law; equations and boundary conditions for**E**in conductors; calculating net resistance; electric power and Joule heat; the RC circuit; the EMF (electromotive «force»). - April 21 (Thursday):
- Second midterm exam.
- April 26 (Tuesday):
- 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. - April 28 (Thursday):
- Time-dependent potentials
*V*(*x,y,x;t*) and**A**(*x,y,x;t*) and gauge transforms (my notes).

Inductance (§7.2.3–4): mutual inductance; self-inductance; the LR circuit; energy stored in an inductor; energy of the magnetic field. - May 3 (Tuesday):
- Maxwell equations (§7.3 and my notes): Maxwell's displacement current; Maxwell–Ampere equation; full set of Maxwell equations; maxwell equations in media; boundary conditions; electromagnetic waves.
- May 5 (Thursday):
- Review.
- Definite plan for May 12 (Thursday):
- Final Exam.

Last Modified: May 5, 2016. Vadim Kaplunovsky

vadim@physics.utexas.edu