Physics 209 Plan
Physics 209: Tentative Plan
Date Description Ref. HW
WEEK 1
8/28 Introduction
8/30 Maxwell's Equations §I
9/1 Electrostatics §1
WEEK 2
9/4 Labor day holiday
9/6 Green Functions §1
9/8 Capacitance and Energy §2 Set 1
WEEK 3
9/11 Method of Images §3
9/13 Spherical Coordinates §2-3
9/15 Corners and Edges §3
WEEK 4
9/18 Conical Holes and Sharp Points §3.4
9/20 A conducting plane with a hole §3.13 Set 2
9/22 Multipole Expansion I §4
WEEK 5
9/25 Multipole Expansion II §4
9/27 Molecular Polarizability §4.5
9/29 Magnetostatics §5
WEEK 6
10/2 Magnetic Dipoles §5 Set 3
10/4 Energy §6
10/6 Momentum §6
WEEK 7
10/9 Vector and Scalar Potentials §6
10/11 The Wave Equation §7 Set 4
10/13 Charged Particle with Constant Velocity §11
WEEK 8
10/16 Cherenkov Radiation §13.4
10/18 Plane Waves §7 Set 5
10/20 Reflection and Refraction §7
WEEK 9
10/23 Dispersive Media I §7
10/25 Dispersive Media II §7
10/27 Radiation §9
WEEK 10
10/30 Electric and Magnetic Dipole Radiation §9 Set 6
11/1 TE and TM modes I §9.7
11/3 Guest lecture: Particle in a magnetic field I §12
WEEK 11
11/6 TE and TM modes II §9.7
11/8 Guest lecture: Lorentz Transformations §11 Set 7
11/10 Veteran's Day
WEEK 12
11/13 Antennas §9.4
11/15 The Gap Equation -
11/17 Worldlines in Special Relativity §14 Set 8
WEEK 13
11/20 Tensors in Special Relativity §12
11/22 Special Relativity and Electromagnetism §12
11/24 Thanksgiving holiday
WEEK 14
11/27 Spin in an electromagnetic field §11.11
11/29 Synchrotron Radiation §14 Set 9
12/1 Synchrotron Radiation §14
WEEK 15
12/4 Introduction to Field Theory §?
12/6 Magnetohydrodynamics §?
12/8 Review II - Set 10
12/13 Final Exam
Ref. - Reference in Jackson.
HW - Homework is due on that date.

More details

Introduction

Organizational issues, general course description, Maxwell's equations, typical values of electric fields, typical values of magnetic fields, regime of applicability of classical E&M.

Maxwell's Equations

Charge quantization, Lorentz force, Macroscopic media, Polarization, Magnetization, relation between D and E, relation between B and H, Electric permittivity, Magnetic permeability, Anisotropic media, Boundary conditions at interfaces, Tests of the inverse square law, Cavendish's experiment, Schumann resonances.

Electrostatics

Laplace and Poisson equations, Dirichlet and Neumann boundary conditions, Green's theorem, Electric dipole moments, Discontinuity of Φ across a layer of dipoles.

Green Functions

Green functions G(x,x') for Poisson's equation with Dirichlet or Neumann boundary conditions, Example in one dimension.

Capacitance and Energy

Coefficients of potential, Coefficients of induction, Capacitances, Electrostatic energy.

Method of Images

Point charge near an infinite conducting plane, Point charge near a grounded conducting sphere, Point charge near a charged conducting sphere, Dirichlet problem for the space outside the sphere.

Spherical Coordinates

Method of Inversion, Legendre Polynomials, Legendre and Associated Legendre equations, Spherical Harmonics, Conducting sphere in a uniform electric field, The WMAP Picture of the Cosmic Microwave Background.

Corners and Edges

Polar coordinates, Behavior of electrostatic fields near corners and edges.

Conical Holes and Sharp Points

Legendre functions of the first kind, Behavior of electrostatic fields near tips of cones.

A conducting plane with a hole

Elliptical coordinates in 2D, Oblate spherical coordinates in 3D, Application to the problem of a conducting plane with a circular hole.

Multipole Expansion I


Multipole Expansion II

Expansion of the potential in multipole coefficients.

Molecular Polarizability

Microscopic versus Macroscopic (mean) field, Average electric field in a spherical region, Clausius-Mossotti equation.

Magnetostatics

Vector potential, Gauge invariance, Coulomb gauge, Bio-Savart law, Force between current loops.

Magnetic dipoles

Magnetic dipole moment, Field of a magnetic dipole, Energy of a magnetic dipole in a magnetic field, Force and torque on a magnetic dipole.

Energy

Energy density, Poynting vector, Energy conservation, Electrostatic and Magnetostatic energy, Self-Inductance, Mutual-Inductance, Ferromagnets, Residual magnetic induction, Coercive "force."

Momentum

Electro-Magnetostatic Momentum density, Momentum conservation, Electro-Magnetostatic stress tensor, A "gas" of photons, The Cosmic Microwave Background Radiation, The 2006 Nobel Prize in Physics.

Vector and Scalar Potentials

Expressions for E and B in terms of the vector and scalar potentials in the time-dependent case, Gauge invariance in the time-dependent case, The Lorenz gauge, The Coulomb (transverse) gauge, The inhomogeneous wave equation, Helmholtz's equation, Retarded and advanced potentials.

The Wave Equation

Helmholtz's equation, Retarded and advanced potentials, Green's function for the wave equation.

Charged Particle with Constant Velocity

Electromagnetic field of a charged particle moving at constant velocity.

Cherenkov Raidation

Cherenkov radiation, Frank-Tamm formula for the radiated energy per unit distance along the path of the particle, Ring Imaging Cherenkov (RICH) detectors, The Super-Kamiokande experiment, (theoretical) proton decay.

The Wave Equation

(Midterm Survey), One-dimensional wave equation, Plane waves, Linear and circular polarization, Phasors, Averages of quadratic expressions.

Reflection and Refraction

Snell's law, Fresnel formulas, Total internal reflection, Brewster angle, Goos-Haenchen effect.

Dispersive Media I

Absorption coefficient, Index of refraction and absorption coefficient of water, Causality, Kramers-Kronig relations.

Dispersive Media II

Derivation of Kramers-Kronig relations, Resonant absorption, Anomalous dispersion, Plasma frequency, Plasma dispersion relation, (Mass gap), Group velocity, Propagation of plane waves through a dispersive medium, Sommerfeld precursor.

Radiation

...

Electric and Magnetic Dipole Radiation

...

TE and TM modes I

...

Particle in a magnetic field I

Prof. Petr Hořava will talk about a particle in a magnetic field.

TE and TM modes II

...

Special Relativity

Prof. Raphael Bousso will talk about special relativity.

Antennas

The antenna as a boundary value problem, center-fed linear antenna, radiated power, angular distribution.

The Gap Equation

skin depth, duality relations for two electromagnetic systems with identical geometries, the Gap Equation for a receiving antenna.

Worldlines in Special Relativity

Lorentz transformations, proper Lorentz transformations, SO(3,1), invariant interval, metric, 4-velocity, 4-acceleration, momentarily comoving reference frame (MCRF).

Tensors in Special Relativity

Definition of tensors, transformation of tensors from one reference frame to another, symmetric tensors, anti-symmetric tensors, field-strength tensor.

Special Relativity and Electromagnetism

Field-strength tensor, transformation of E and B, 4-current, Maxwell's equations in tensor form, 4-potential, magnetization-polarization tensor, Green's function for the wave equation D(x,x').

Spin in an electromagnetic field

Anomalous Zeeman effect, spin-orbit interaction, BMT equation, measurement of the anomalous gyromagnetic ratio g for the electron, Penning trap, the 1989 Nobel prize in physics, precession of the polarization, measurement of the anomalous gyromagnetic ratio g for the muon (the scientific paper is arXiv:hep-th/0401008).