Lecture Notes

Lecture Notes

PHY 415: Electromagnetic Theory I
Prof. S. Teitel stte@pas.rochester.edu ---- Fall 2019

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, Coulomb's law, the electric field, differential and integral form of Maxwell's equations for electrostatics
Lecture 2 - From Coulomb to Maxwell: Helmholtz's Theorem, Lorentz force, the magnetic field, Biot-Savart law, current density, local charge conservation and the definition of magnetostatics, Maxwell's equations for magnetostatics
Lecture 3 - Faraday's Law, Maxwell's correction to Ampere's Law, EM waves, systems of units, scalar and vector potentials in statics, potentials and gauge invariance in dynamics
Lecture 4 - Lorentz gauge, Coulomb gauge, longitudinal and transverse parts of a vector function, review of Fourier transforms
Lecture 5 - Physical meaning of the electrostatic potential, Green's function, conductors in electrostatics, Coulomb problem as a boundary value problem, electric field at a charged surface, Dirichlet vs Neumann boundary condition, examples
Lecture 6 - Green's identities, uniquness of solutions to the Dirichlet and Neumann boundary value problem, Greens functions for Dirichlet and Neumann boundary conditions, the image charge method for a charge in front of an infinite grounded plane
Lecture 7 - The image charge method for a charge in front of a grounded, a charged, and a neutral conducting sphere
Lecture 8 - Separation of variables method in rectangular and polar coordinates, electric field at a sharp edge
Lecture 9 - Separation of variables in spherical coordinates, Legendre polynomials, examples of problems with azimuthal symmetry.
Green's functions, part III - Eigenfunction expansion for the Greens function - we did not go over this in lecture, but it is nevertheless something you should know about!
Lecture 10 - Uniformly polarized sphere, electrostatic multipole expansion, monopole, dipole, quadrupole moments
Lecture 11 - Dependence of multipoles on the choice of coordinate origin, electric quadrupole example, general form for the angular distribution of the quadrupole term and why trace[Q]=0.
Lecture 12 - Some additional points on the electrostatic multipole expansion, magnetostatic multipole expansion, magnetic dipole approximation, magnetic dipole for a flat planar loop
Lecture 13 - Magnetostatic scalar potential, boundary conditions at a sheet current, examples
Lecture 14 - Symmetry under parity transformations, vectors and psuedovectors, macroscopic Maxwell's equations, dielectrics, polarization density, electric displacement vector D
Lecture 15 -Bound surface charge density, magnetic materials, average microscopic current
Lecture 16 - Magnetization density and bound current, the magnetic field H, conservation of bound charge, bound surface current, vanishing of total bound charge and bound current, boundary conditions
Lecture 17 - Linear materials, electric and magnetic susceptibilities, dielectric constant, magnetic permeability, atomic polarizability and the Clausius-Mossotti equation, screening of free charge, examples, a point charge in a dielectric sphere
Lecture 18 - A point charge in a dielectric sphere, bar magnets, electromagnetism and conservation of energy
Lecture 19 - Electromagnetic energy density, Poynting vector, conservation of momentum, Maxwell stress tensor, force on a conducting surface
Lecture 20 - 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 21 - Energy and momentum of electromagntic waves in a vacuum, frequency dependent atomic polarizability, complex frequency dependent dielectric function
Lecture 22 - Electromagnetic waves in a dielectric, dispersion relation, phase velocity, group velocity, normal and anomalous dispersion, transparent propagation, resonant absorption, total reflection
Lecture 23 - Electromagnetic waves in conductors, frequency dependent conductivity, low frequency "good" conductors, skin depth, high frequencies, longitudinal modes and plasma oscillations
Lecture 24 - Linear, circular and elliptical polarization, waves at interfaces, angles of incidence, reflection and transmission, Snell's law, total internal reflection
Lecture 25 - Snell's law for dissipative media, coefficient of reflection, total reflection, Brewster's angle
Lecture 26 - Green's function for the wave equation, Lienard-Weichert potentials for a moving charged particle, potentials from a point charged particle moving with constant velocity
Lecture 27 - Radiation from a source oscillating with simple harmonic motion, electric dipole, magnetic dipole, and electric quadrupole radiation, radiated E and B fields in the electric dipole approximation
Lecture 28 - Poynting vector, and radiated power from an oscillating source in the electric dipole, magnetic dipole, and electric quadrupole approximations, radiation from a general time dependent source, Larmor's formula for radiation from an accelerating charge
Lecture 29 - Special relativity, Lorentz transformation, 4-vectors, proper time, 4-velocity, 4-gradient, 4-current, 4-potential
Lecture 30 - Field strength tensor, dual field strength tensor, and Maxwell's equations, transformation of E and B fields, 4-momentum, Minkowski force, Lorentz force, relativistic Larmor's formula