Lecture, date |
Subject |
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Electrodynamics. Putting the
finishing touches on Maxwell's equations, we complete the foundations of electrodynamics,
in preparation for the study of light. |
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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. |
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46 |
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 |
47 |
28 January |
Transverse waves and
polarization. Boundary conditions for transverse waves, reflection and transmission. |
Griffiths, pp. 370-374;
Crawford, pp. 394-406 |
48 |
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 |
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. 382-390;
Crawford, pp. 243-248 |
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 finite-thickness linear media; antireflection
coatings, dielectric multilayers. |
Crawford, pp.
245-252 |
53 |
11 February |
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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. Frequency-dependent conductivity, dielectric constant and permeability. Group velocity. |
Griffiths, pp. 398-399;
Purcell, pp. 298-318 |
57 |
20
February |
Nonconducting media: anomalous
dispersion, absorption, Cauchy's equation. |
Griffiths, pp. 399-404;
Crawford, pp. 176-184 |
58 |
23
February |
Dispersion in conductors.
Plasma frequency. Example of the ionosphere. |
Crawford, pp. 184-191 |
59 |
25
February |
Waveguides. TE and TM
modes in rectangular waveguides. |
Griffiths, pp. 405-410;
Crawford, pp. 337-342 |
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 |
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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. |
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61 |
1
March |
Retarded potentials. Cause and
effect in electrodynamics. |
|
62 |
3
March |
Electric dipole radiation.
Spherical waves. Near-field and far-field domains. Dipole antennas. |
Griffiths, pp. 443-449;
Crawford, pp. 366-378 |
63 |
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 |
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 Liènard-Wiechert 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 Abraham-Lorentz formula for
the radiation-reaction 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: far-field (Frauenhofer) diffraction. |
Crawford, pp. 478-491 |
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 |
|
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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. |
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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 |
Four-vectors and their Lorentz
transformations. Covariant and contravariant four-vectors. Invariant intervals. Spacetime
diagrams; world lines and the light cone. |
|
78 |
16
April |
The four-velocity and
energy-momentum four-vectors. 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. 522-525;
Purcell, pp. 176-199 |
82 |
26
April |
Relativistic transformation of
the electric and magnetic fields. |
Griffiths, pp. 525-532;
Purcell, pp. 235-241 |
83 |
28
April |
The electromagnetic field
tensor; the equations of electrodynamics in tensor notation |
|
Final Examination, covering the entire course |
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