Physics 505

Week 1: 1/22

• Units
• Overview: Specify the currents (or a constituent relation) and solve for the fields
• Basic vector analysis, tensors, "bac-abc":
  • A slower treatment of tensors was in first two lectures of math phys: l1,l2
• Helmholtz theorem's and consequences
  • Gauge invariance
  • Current conservation
• Expansion of the Maxwell equations in 1/c

Week 1: 1/22

• 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 and Sturm Liouville Equations
  • Separation of Variables in cartesian coordinates. Self adjoint operators
  • Green functions of of 1D second order differential equations
  • Finding green functions with separation
• Separation of variables in Spherical Coordinates:
  • Separation in spherical coordinates. Sphere in an electric field
  • A charged spherical shell
  • Free green functions by separation and the multipole identity
  • Multipole expansion again, but with spherical harmonics
• A charged ring in a sphere, a good example:
  • Green function for a charged ring in a grounded sphere
  • The force and analysis of induced charge
• A charged cylindrical shell and modified bessel functions

• Constitutive relations and symmetry
• 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
  • Solving the separated vector potential equations
  • The scalar potential for magnetostatics (skipped)
  • 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 example
• 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, 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