Lecture Notes

Lecture Notes

PHY 415: Electromagnetic Theory I
Prof. S. Teitel stte@pas.rochester.edu ---- Fall 2011

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, Faraday's Law, Maxwell's correction to Ampere's Law, EM waves
Lecture 3 - Systems of units, scalar and vector potentials, gauge invariance, Lorentz gauge, Coulomb gauge
Lecture 4 - Longitudinal and transverse parts of a vector function, review Fourier transforms, physical meaning of the electrostatic potential, Green's function, conductors in electrostatics
Lecture 5 - Coulomb problem as a boundary value problem, electric field at a charged surface, Dirichlet vs Neumann boundary condition, examples, Green's identities and uniqueness
Green's functions, part II - Greens functions for Dirichlet and Neumann boundary conditions - we will 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, Legendre polynomials
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 9 - Multipole expansion: monopole, dipole and quadrupole moments
Lecture 10 - Multipole expansion continued, magnetostatics, magnetic dipole approximation
Lecture 11 - Magnetostatic scalar potential, boundary conditions at a sheet current, examples
Lecture 12 - Symmetry under parity transformations, Macroscopic Maxwell's equations: dielectrics
Lecture 13 - Macroscopic Maxwell's equations: polarization density, electric dispacement field D, magnetic materials, paramagnetism and diamagnetism, bound currents
Lecture 14 - Macroscopic Maxwell's equations: magnetization density, H field, bound surface current, conservation of bound charge, boundary conditions
Lecture 15 - Linear Materials: electric and magnetic susceptibilities, dielectric constant, magnetic permeability, atomic polarizability and the Clausius-Mossotti equation, boundary condition problems
Lecture 16 - Point charge in a dielectric sphere, bar magnets, electromagnetism and conservation of energy
Lecture 17 - Electromagnetic energy density, Poynting vector, conservation of momentum, Maxwell stress tensor, force on a conducting surface
Lecture 18 - Capacitance matrix, inductance matrix, electromagnetic waves in a vacuum
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 - Energy and momentum in electromagntic waves, frequency dependent atomic polarizability, frequency dependent dielectric function
Lecture 20 - Electromagnetic waves in a dielectric: transparent propagation, resonant absorption, total reflection
Lecture 21 - Electromagnetic waves in conductors: frequency dependent conductivity, low frequency "good" conductors, skin depth, high frequencies, longitudinal modes and plasma oscillations
Lecture 22 - Linear, circular and elliptical polarization, waves at interfaces, angles of incidence, reflection and transmission
Lecture 23 - Snell's law for transparent and dissipative media, total internal reflection, coefficient of reflection
Lecture 24 -Total reflection, Brewster's angle, Kramers-Kronig relation, Green's function for the wave equation
Lecture 25 - Lienard-Weichert potentials for a moving charged particle, potentials from a particle moving with constant velocity, radiation from a source oscillating with simple harmonic motion
Lecture 26 - Electric dipole, magnetic dipole, and electric quadrupole radiation; fields, Poynting vector and radiated power
Lecture 27 - Radiation from a general time dependent source, Larmor's formula for radiation from an accelerating charge, special relativity, Lorentz transformation, 4-vectors
Lecture 28 - Proper time, 4-velocity, 4-gradient, 4-current, 4-potential, field strength tensor and Maxwell's equations
Lecture 29 - Energy-momentum 4-vector, Lorentz force, relativistic Larmor's formula