Physics 505

Week 1: 8/25
part 1

• Units
• Overview: Specify the currents (or a constituent relation) and solve for the fields
• Vector analysis, tensors, "bac-abc", Helmholtz theorems and immediate applications:
  • Gauge invariance
  • Current conservation
  • Waves
• Expansion of the Maxwell equations in 1/c

Week 1: 8/25
part 2

• Fundamental equations and boundary conditions
• Electrostatic energy
• Stress and force in electrostatics:
  • The stress tensor and forces generally, momentum conservation law
  • The electric stress tensor and two in class problems
• The multipole expansion
• Forces on a multipole

• Intro to Green Functions and Image Charges
• Green Theorem
  • Example
  • Proof
• Separation of Variables for BVP
• Eigen function expansions
• Separation of Variables in cartesian coordinates. Self adjoint operators
• Separation in spherical coordinates. Jump conditions in a charged sphere
• Legendre polynomials. Azimuthal symmetry and a sphere in an electric field
• Green functions by separation, and the multipole identity
• Multipole expansion with Sphereical Harmonics
• A charged ring in a sphere
  • Green Function for a charged ring in a grounded sphere, Sturm Liouville Theory
  • The force and analysis of induced charge
• A charged cylindrical shell and modified bessel functions

• A consitutive relation for the current in electric fields
  • Determining the current -- the polarization vector
  • The material charge density in the bulk and interfaces
  • Relation to the dipole picture
• Boundary value problems with dielectrics
• Energy and stress in dielectrics

Magnetostatics:

• Ohms Law and steady currents
• Basics
  • Expansion of the Maxwell Equations in 1/c
  • Amperes Law and Biot Savat
  • Gauge Potentials and the Coulomb Gauge
• Magnetic Multipoles
  • Field from a multipole
  • Force and torque on a multipole
• Boundary conditions in magnetostatics
  • Boundary conditions
  • a spinning sphere
• Magnetic Fields in matter:
  • A derivative expansion for the constitutive relation
  • The magnetization and associated boundary currents
  • The equations of linearized magneto statics
  • The magnetic scalar potential
  • Diamagnetic, Paramagnetic, and Ferromagnetic substances

Quasi-statics in vacuum and metals. Maxwell Equations for Potentials.

• Basics of Induction:
  • The maxwell equations expansion to 1/c^2
  • Energy stored in magnetic field.
  • Mutual inductance
• The Maxwell equations for the gauge potentials and quasistatics.
• Quasi-static fields in metals

• Conservation Laws
• Basics of Waves
• Reflection at Interfaces
• Waves in Metals and Reflection

• Linear response. Waves in dispersive media
• Lorentz model for insulators and metals
• Wave packets, group velocity, and phase shifts
• Kramers Kronig relations

• Simple Harmonic Oscillator
• The wave equation
• Green theorem notes

• Radiation fields, and technical note
• Larmour formula and electric dipole radiation
• Magnetic dipole and quadrupole radiation
• Antennas

• Introduction and Manifest Covariance. In-class problems
• Electrodynamics in Covariant Form:
  • The sourced (i.e. current driven) Maxwell equations
  • The unsourced Maxwell equations and the Bianchi identity
  • The stress tensor
  • One line problems.
• Transformations of fields.
  • Fields of fast particles
  • Constituent relations of moving bodies
• Relativistic action and Hamiltonian for particles.
• Relativistic action for the fields.

• The fields of point particle
  • Lienard-Wiechert potentials and fields.
  • The power during radiated by relativistic charged particles.
  • Circular versus Linear Accelerators.
• The frequency spectrum in relativistic radiation, with applications to synchrotron radiation.
  • The frequency spectrum associated with relativistic charged particles
  • Qualitative estimates of synchrotron radiation.
  • Quantitive calculations of sychrotron radiation.
• The bremsstrahlung spectrum
  • The spectrum of photons accompanying a collision.
  • Number of photons in a bremsstrahlung cone.
  • Number of bremsstrahlung photons with a given polarization.

• Overview
  • Cross sections
  • The Thompson cross section and associated polarizations
• Dipole scattering
• Born approximation