Physics 7410 Fall 2014 Syllabus

Note: a substantial fraction of this course will cover basic mathematical techniques equally relevant to quantum mechanics and to other branches of physics. I will on occasion follow my online quantum mechanics notes for some of these topics.

0. Jackson’s Introduction and Survey

 A first look at:

Maxwell’s equations in vacuum and their experimental basis:

(a) inverse-square Coulomb law: how well verified? Range of validity?

(b) linear superposition: how well verified? Range of validity?

Maxwell’s equations in macroscopic media, and boundary conditions at interfaces.

Now we get serious…

1. Electrostatics

Coulomb’s law, Electric field, Gauss’ law, both integral and differential forms, the potential.

Some essential mathematics: Poisson equation, Laplace equation, the delta function, Green’s theorem and functions, Dirichlet and Neumann boundary conditions.

Electrostatic potential energy, energy density, capacitance.  Small variation from true minimum gives Poisson’s equation.

Variational methods? Relaxation?

2. Boundary Value Problems in Electrostatics I

Image charges in planes and spheres.

Orthogonal polynomial, Fourier Series.

Separation of variables.

Mathematical interval: functions of a complex variable.

Two-dimensional electrostatics using complex variable techniques (not in Jackson).

3. Boundary Value Problems in Electrostatics II

Spherical and cylindrical coordinates. Spherical harmonics. Bessel functions. Eigenfunction expansion of Green’s function.

Physics example: circular hole in plane conductor.

4. Multipoles, Electrostatics of Macroscopic Media, Dielectrics.

Multipole expansion of field from a given static charge distribution (monopole, dipole, quadrupole…).

Dielectrics: the electric field inside, boundary conditions, microscopic models (polarizable molecules), energetics. 

5. Magnetostatics, Faraday’s Law, Quasi-Static Fields

Biot-Savart law and its relation to field from a single moving charge.

Interaction between current loops.

Vector potential, magnetic induction (meaning field like, not Faraday’s induction).

Fields of a localized current distribution, magnetic moment, forces on such a distribution from an external field.

Macroscopic equations, ferromagnets, boundary conditions.

Boundary value problems: vector potential and magnetic scalar potential methods.

Uniformly magnetized sphere.  Same in external field. Spherical shell magnetic shielding.

Faraday’s law of induction. Field energy.  Self and mutual induction.

Quasi statics: eddy currents, skin depth.

6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws.

Displacement current.

Vector and scalar potentials, Gauge transformations.

Green’s function for waves.  Retarded function.  Schott’s formulae (Zangwill p 726).

Macroscopic electromagnetism.

Poynting’s Theorem.

E&M symmetries: inversion, time reversal.  Magnetic monopoles, Dirac’s argument.

7. Plane Electromagnetic Waves and Wave Propagation

Waves in a nonconducting medium. Stokes’ polarization parameters.

Reflection and refraction at a plane interface between dielectric media.

Frequency dependence of dispersion in dielectrics, conductors, plasmas.

Possibly Kramers-Kronig.

Graduate E&M first half: Electrostatics, Magnetostatics, Induction, Maxwell's Equations, Waves.