## Lecture Notes and Tentative Schedule

These are lecture notes that I use. They are not a substitute for a good book or for going to class. But, if you miss one class they can work for you

#### Overivew

 Week 1: 1/22 The Maxwell equations and mathematical review: 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

#### Electrostatics

 Week 1: 1/22 Electrostatics: 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 Week 2: 1/29 Methods of Electrostatics Intro to Green Functions and Image Charges Green Theorem Example Proof Separation of Variables for BVP: Separation of variables in Spherical Coordinates: A charged ring in a sphere, a good example: A charged cylindrical shell and modified bessel functions Week 3: 2/5 Week 2 continued

#### Electrostatics in media

 Week 4: 2/12 Electrostatics in Material: 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

 Week 5: 2/19 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

#### Induction, Conservation Laws, Waves

 Week 6: 2/26 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 Week 7: 3/5 Conservation Laws. Propagation of waves in media and interfaces: Spring Break: 3/12--3/18 Week 8: 3/19 Dispersion. Wave packtes.