Lecture Notes

Lecture Notes

PHY 415: Electromagnetic Theory I
Prof. S. Teitel stte@pas.rochester.edu ---- Fall 2010

Lecture Notes

My hand written class lecture notes are being scanned and uploaded for you to view. Please be warned that these are the notes I prepare for myself to lecture from - they are not in general carefully prepared for others to read. I make no guarantees about their legibility, or that they are totally free of errors. I hope, nevertheless that you will find them useful. The lectures are uploaded as pdf files, so you will need Adobe Acrobat Reader in order to read them. You can download Acrobat Reader for free here.

The lecture note files correspond roughly to the material presented in a given day's lecture. But you may on occassion find the end of one day's lecture at the start of the file for the next day's lecture, so please look there if you think there might be something missing.

Lecture 0 - A brief history of electromagnetism
Lecture 1 - From Coulomb to Maxwell: charge, Coulombs law, the electric field, differential and integral form of Maxwell's equations for electrostatics
Lecture 2 - From Coulomb to Maxwell: Lorentz force, the magnetic field, current density, charge conservation and the definition of magnetostatics, Maxwell's equations for magnetostatics
Lecture 3 - Faraday's Law, Maxwell's correction to Ampere's Law, systems of units, scalar and vector potentials, gauge invariance, Lorentz gauge
Lecture 4 - Coulomb gauge, longitudinal and transverse parts of a vector function, review Fourier transforms, physical meaning of the electrostatic potential, Green's function
Lecture 5 - Coulomb problem as a boundary value problem, properties of conductors in electrostatics, electric field at a charged surface, Dirichlet vs Neumann boundary condition, examples, Green's identities and uniqueness
Green's functions, part II Greens function for Dirichlet and Neumann boundary conditions - we did not go over this in lecture.
Lecture 6 - The image charge method for a charge in front of an infinite plane, and in front of a conducting sphere
Lecture 7 - Separation of variables method in rectangular and polar coordinates
Lecture 8 - Separation of variables method in spherical coordinates
Lecture 9 - Separation of variables method in spherical coordinates continued, multipole expansion
Green's functions, part III Eigenfunction expansion for the Greens function - we did not go over this in lecture, but it provides some of the theoretical basis for why the separation of variables method works
Lecture 10 - Multipole expansion continued
Lecture 11 - Magnetostatics: multipole expansion and the magnetic dipole moment
Lecture 12 - Magnetostatic scalar potential, boundary conditions at a sheet current, examples, symmetry under parity transformations
Lecture 13 - Macroscopic Maxwell's equations: dielectrics, polarization density, displacement field D
Lecture 14 - Macroscopic Maxwell's equations: magnetic materials, paramagnetism and diamagnetism, magnetization density, H vs B
Lecture 15 - Macroscopic Maxwell's equations: bound surface current, conservation of bound charge, boundary conditions
Lecture 16 - Linear Materials: electric and magnetic susceptibilities, dielectric constant, magnetic permeability, atomic polarizability and the Clausius-Mossotti equation, boundary condition problems, bar magnets
Lecture 17 - Electromagnetic energy density, Poynting vector, conservation of energy
Lecture 18 - Conservation of momentum, Maxwell stress tensor, force on a conducting surface, capacitance matrix, inductance matrix
Supplement - Force, torque, and interaction energy for electric and magnetic dipoles in an external field - we did not go over this in lecture.
Lecture 19 - Electromagnetic waves in a vacuum, frequency dependent atomic polarizability
Lecture 20 - Electromagnetic waves in a dielectric, frequency dependent dielectric function, phase and group velocity, attenuation, transparent propagation
Lecture 21 - Electromagnetic waves in a dielectric continued: resonant absorption, total reflection; waves in conductors: frequency dependent conductivity, low frequency "good" conductors, skin depth
Lecture 22 - Electromagnetic waves in conductors continued: high frequencies, plasma oscillations, linear, ellipitcal and circular polarization
Lecture 23 - Reflection and transmission of waves at interfaces, Snell's law and its analog for a dissipative material, total internal reflection
Lecture 24 - Reflection of electromagnetic waves at an interface, total reflection, Brewster's angle, Kramers-Kronig relation
Lecture 25 - Green's function for the wave equation, Lienard-Weichert potentials for a moving charged particle, potentials from a particle moving with constant velocity
Lecture 26 - Radiation from a source oscillating with simple harmonic motion, electric dipoie, magnetic dipole, electric quadrupole radiation
Lecture 27 - Poynting vector and radiated power, radiation from arbitrary sources, Larmor's formula
Lecture 28 - Special relativity, Lorentz transformation, 4-vectors, 4-current, 4-potential
Lecture 29 - Field strength tensor and Maxwell's equations, energy-momentum 4-vector, Lorentz force, relativistic Larmor's formula