Lecture, date



Electrodynamics. Putting the finishing touches on Maxwell's equations, we complete the foundations of electrodynamics, in preparation for the study of light.


14 January

Displacement current, Maxwell's repair of Ampère's Law, and the final version of Maxwell's equations.

Griffiths, pp. 321-330


16 January

Boundary conditions. The potentials V and A in electrodynamics.

Griffiths, pp. 331-333


21 January

Gauge transformations; the Coulomb and Lorentz gauges. Force, momentum and energy in electrodynamics.

Griffiths, pp. 345-349, 416-422


23 January

Conservation of momentum and energy in electrodynamics: Poynting's theorem, the Maxwell stress tensor. Review of the various systems of units in use with electrodynamics.

Griffiths, pp. 349-359, 558-561

Electromagnetic Waves. We derive a wave equation from Maxwell's equations, solve it, and from the solutions we obtain a description of the basic properties of light: refraction, reflection, absorption, dispersion, polarization and interference.


26 January

The wave equations in electrodynamics and in mechanics (waves on a string), and the simplest solutions. Phase velocity.

Griffiths, pp. 364-370; Crawford, pp. 50-59


28 January

Transverse waves and polarization. Boundary conditions for transverse waves, reflection and transmission.

Griffiths, pp. 370-374; Crawford, pp. 394-406


30 January

Analogy between waves on a string and those in electrical circuits: reflection and transmission of impedance discontinuities. Impedance matching.

Crawford, pp. 191-196, 226-240


2 February

Propagation of plane electromagnetic waves in vacuum; energy and momentum of plane waves.

Griffiths, pp. 374-382


4 February

Plane electromagnetic waves in linear media. Reflection and transmission for normal incidence on dielectric surfaces. Fresnel's equations for the reflection and transmission coefficients of light at oblique incidence. Snell's Law.

Griffiths, pp. 382-390; Crawford, pp. 243-248


6 February

Consequences of the Fresnel equations: total internal reflection, polarization on reflection and Brewster's angle. Interference.

Griffiths, pp. 390-392; Crawford, pp. 342-346, 407-419


9 February

Interference in stratified linear media: multilayer boundary conditions, characteristic matrix formulation. Transmission and reflection by finite-thickness linear media; antireflection coatings, dielectric multilayers.

Crawford, pp. 245-252; Hecht, pp. 426-430; or Watson, here.


11 February


13 February

Electromagnetic waves in conducting media. Attenuation of the waves within the conductor: skin depth.

Griffiths, pp. 392-395


16 February

Reflection and transmission by conducting surfaces. Characteristic matrix for conducting layers.

Griffiths, pp. 396-398


 18 February

Dispersion relations. Frequency-dependent conductivity, dielectric constant and permeability. Group velocity.

Griffiths, pp. 398-399; Purcell, pp. 298-318


 20 February

Nonconducting media: anomalous dispersion, absorption, Cauchy's equation.

Griffiths, pp. 399-404; Crawford, pp. 176-184


 23 February

Dispersion in conductors. Plasma frequency. Example of the ionosphere.

Crawford, pp. 184-191


 25 February

Waveguides. TE and TM modes in rectangular waveguides.

Griffiths, pp. 405-410; Crawford, pp. 337-342


 27 February

TEM waveguide modes: their absence in hollow metallic waveguides, and their presence in coaxial metallic and hollow dielectric waveguides

Griffiths, pp. 411-412


 27 February

Midterm examination on all material covered to date


Electromagnetic Radiation. Here we receive an introduction to some of the most interesting electromagnetic phenomena, involving radiation of electromagnetic waves by moving charges, and scattering and diffraction of light by apertures and obstructions. This includes a description of rainbows, and the reason for the blue color and polarization of the sky. In the discussion of radiation-reaction forces, we also discover some interesting apparent limitations to classical electrodynamics.


 1 March

Retarded potentials. Cause and effect in electrodynamics.

Griffiths, pp. 422-428


 3 March

Electric dipole radiation. Spherical waves. Near-field and far-field domains. Dipole antennas.

Griffiths, pp. 443-449; Crawford, pp. 366-378


 5 March

Cross section of dipole radiators. Rayleigh's explanation of the blue sky. Magnetic dipole radiation.

Griffiths, pp. 451-454; Crawford, pp. 378-380


 15 March

Radiation from arbitrary charge and current distributions. Larmor's formula for the radiated power.

Griffiths, pp. 454-458


 17 March

Retarded potentials for a point charge in motion. The Liènard-Wiechert formulae.

Griffiths, pp. 429-434


 19 March

Derivation of the fields from a moving point charge.

Griffiths, pp. 435-440


 22 March

Power radiated by point charges in motion: bremsstrahlung and synchrotron radiation.

Griffiths, pp. 460-464


 24 March

The Abraham-Lorentz formula for the radiation-reaction force. Radiation damping.

Griffiths, pp. 465-468


 26 March

The origin of radiation reaction; a fundamental inconsistency of classical electrodynamics with Newton's third law?

Griffiths, pp. 469-472


 29 March

Application of Huygens' principle to electromagnetic waves: far-field (Frauenhofer) diffraction.

Crawford, pp. 478-491; Hecht, pp. 443-445


 31 March

Diffraction from a square aperture or square obstacle. Babinet's principle.

 Hecht, pp. 464-467, 508-509


 2 April

Diffraction from a circular aperture: dark rings and the Airy disk. Angular resolution of the eye and of telescopes.

 Hecht, pp. 467-474


 5 April

Application of refraction, interference and diffraction: the optics of raindrops, and how rainbows and glories work



 7 April 2004


Electrodynamics and Relativity. Maxwell's equations, as we have written them already, are invariant under Lorentz transformations; therefore the special theory of relativity is already built into our description of electrodynamics. Here we will review special relativity, introduce four-vector and tensor notation, and explore the reasons that relativity came to be incorporated without any deliberate effort on our part.


 9 April

The special theory of relativity: Einstein's postulates, relativity of simultaneity, time dilation, Lorentz contraction

Griffiths, pp. 477-493


 12 April

The Lorentz transformations and the velocity addition rule.

Griffiths, pp. 493-498


 14 April

Four-vectors and their Lorentz transformations. Covariant and contravariant four-vectors. Invariant intervals. Spacetime diagrams; world lines and the light cone.

Griffiths, pp. 500-506


 16 April

The four-velocity and energy-momentum four-vectors. Proper time.

Griffiths, pp. 507-511


 19 April

Energy and momentum conservation in relativity: annihilation, pion decay, Compton scattering.

Griffiths, pp. 511-515


 21 April

Force and momentum in relativity: inapplicability of Newton's third law; the Minkowski force.

Griffiths, pp. 516-521


 23 April

The relativistic invariance of electric charge. Magnetism as a relativistic phenomenon.

Griffiths, pp. 522-525; Purcell, pp. 176-199


 26 April

Relativistic transformation of the electric and magnetic fields.

Griffiths, pp. 525-532; Purcell, pp. 235-241


 28 April

The electromagnetic field tensor; the equations of electrodynamics in tensor notation

Griffiths, pp. 535-540


 6 May

Final Examination, covering the entire course