Lecture, date 
Subject 

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

42 
14 January 
Displacement current, Maxwell's
repair of Ampère's Law, and the final version of Maxwell's equations. 

43 
16 January 
Boundary conditions. The potentials V and A in electrodynamics. 

44 
21 January 
Gauge transformations; the
Coulomb and Lorentz gauges. 

45 
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. 

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. 

46 
26 January 
The wave equations in
electrodynamics and in mechanics (waves on a string), and the simplest solutions. Phase
velocity. 
Griffiths, pp. 364370;
Crawford, pp. 5059 
47 
28 January 
Transverse waves and
polarization. Boundary conditions for transverse waves, reflection and transmission. 
Griffiths, pp. 370374;
Crawford, pp. 394406 
48 
30 January 
Analogy between waves on a
string and those in electrical circuits: reflection and transmission of impedance
discontinuities. Impedance matching. 
Crawford, pp. 191196, 226240 
49 
2 February 
Propagation of plane
electromagnetic waves in vacuum; energy and momentum of plane waves. 

50 
4 February 
Plane electromagnetic waves in
linear media. Reflection and transmission for normal incidence on dielectric surfaces. 
Griffiths, pp. 382390;
Crawford, pp. 243248 
51 
6 February 
Consequences of the Fresnel
equations: total internal reflection, polarization on reflection and Brewster's angle. 

52 
9 February 
Interference in
stratified linear media: multilayer boundary conditions, characteristic matrix
formulation. Transmission and reflection by finitethickness linear media; antireflection
coatings, dielectric multilayers. 
Crawford, pp.
245252 
53 
11 February 

54 
13 February 
Electromagnetic waves in
conducting media. Attenuation of the waves within the conductor: skin depth. 

55 
16 February 
Reflection and transmission by conducting surfaces. Characteristic matrix for conducting layers. 

56 
18
February 
Dispersion relations. Frequencydependent conductivity, dielectric constant and permeability. Group velocity. 
Griffiths, pp. 398399;
Purcell, pp. 298318 
57 
20
February 
Nonconducting media: anomalous
dispersion, absorption, Cauchy's equation. 
Griffiths, pp. 399404;
Crawford, pp. 176184 
58 
23
February 
Dispersion in conductors.
Plasma frequency. Example of the ionosphere. 
Crawford, pp. 184191 
59 
25
February 
Waveguides. TE and TM
modes in rectangular waveguides. 
Griffiths, pp. 405410;
Crawford, pp. 337342 
60 
27
February 
TEM waveguide modes: their absence in hollow
metallic waveguides, and their presence in coaxial metallic and hollow dielectric
waveguides 

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 radiationreaction forces, we also discover some interesting apparent limitations to
classical electrodynamics. 

61 
1
March 
Retarded potentials. Cause and
effect in electrodynamics. 

62 
3
March 
Electric dipole radiation.
Spherical waves. Nearfield and farfield domains. Dipole antennas. 
Griffiths, pp. 443449;
Crawford, pp. 366378 
63 
5
March 
Cross section of dipole
radiators. Rayleigh's explanation of the blue sky. Magnetic dipole radiation. 
Griffiths, pp. 451454;
Crawford, pp. 378380 
64 
15
March 
Radiation from arbitrary charge
and current distributions. Larmor's formula for the radiated power. 

65 
17
March 
Retarded potentials for a point
charge in motion. The LiènardWiechert formulae. 

66 
19
March 
Derivation of the fields from a
moving point charge. 

67 
22
March 
Power radiated by point charges
in motion: bremsstrahlung and synchrotron radiation. 

68 
24
March 
The AbrahamLorentz formula for
the radiationreaction force. Radiation damping. 

69 
26
March 
The origin of radiation
reaction; a fundamental inconsistency of classical electrodynamics with 

70 
29
March 
Application of Huygens'
principle to electromagnetic waves: farfield (Frauenhofer) diffraction. 
Crawford, pp. 478491 
71 
31
March 
Diffraction from a square
aperture or square obstacle. Babinet's principle. 

72 
2
April 
Diffraction from a circular
aperture: dark rings and the Airy disk. Angular resolution of the eye and of telescopes. 

73 
5
April 
Application of
refraction, interference and diffraction: the optics of raindrops, and how rainbows and
glories work 

74 


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 fourvector and tensor
notation, and explore the reasons that relativity came to be incorporated without any
deliberate effort on our part. 

75 
9
April 
The special theory of
relativity: Einstein's postulates, relativity of simultaneity, time dilation, Lorentz
contraction 

76 
12
April 
The Lorentz transformations and
the velocity addition rule. 

77 
14
April 
Fourvectors and their Lorentz
transformations. Covariant and contravariant fourvectors. Invariant intervals. Spacetime
diagrams; world lines and the light cone. 

78 
16
April 
The fourvelocity and
energymomentum fourvectors. Proper time. 

79 
19
April 
Energy and momentum
conservation in relativity: annihilation, pion decay, 

80 
21
April 
Force and momentum in
relativity: inapplicability of 

81 
23
April 
The relativistic invariance of
electric charge. Magnetism as a relativistic phenomenon. 
Griffiths, pp. 522525;
Purcell, pp. 176199 
82 
26
April 
Relativistic transformation of
the electric and magnetic fields. 
Griffiths, pp. 525532;
Purcell, pp. 235241 
83 
28
April 
The electromagnetic field
tensor; the equations of electrodynamics in tensor notation 

Final Examination, covering the entire course 