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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