| Day, Date, Year | Lecture Content and Homework Assignment |
|---|---|
| Mon. Jan. 12, 2015 |
Lecture: Introduction to frequency dependence of the refractive index
via the spring model of an atom. Homework (HW #1): Consider a hydrogen atom in its ground state. (a) Using the ground-state wavefunction, show that the restoring force for displacements small compared to the Bohr radius obeys Hooke's Law. Find the spring constant and the natural frequency. (b) For such an atom in the atmosphere, bathed in sunlight, would the displacement actually be small compared to the Bohr radius? [For the electric field amplitude you may use, for instance, the answer to last semester's homework of Dec. 1.] |
| Wed. Jan. 14, 2015 |
Lecture: Refractive index as a function of frequency for non-permeable
media. Homework (HW #1): [Due to difficulty of obtaining data, this problem has been suspended. If a useful data table is found, it may be reinstated later.] Pick a multi-electron gas (He and beyond) at STP and apply Jackson's eq. (7.51) as best as you can, by finding values of the various constants therein, and see how well it predicts the actual dielectric constant. Good luck on your choice of gas! Don't pick the same gas as anyone else you know! |
| Fri. Jan. 16, 2015 (WK1) |
Lecture: Low and high frequency limits of the dielectric constant
expression. Conductivity and refractive index of metals and plasmas. Homework (HW #1): Jackson 7.4. |
| Tue. Jan. 20, 2015 |
Lecture: A lightning review of Special Relativity. Homework (HW #2): No Homework. |
| Wed. Jan. 21, 2015 |
Lecture: The various effects and their characteristic times that
determine time-varying fields in conductors: charge clearing,
collisions, plasma oscillations, Ohm's Law, diffusion of fields,
energy loss due to electrical resistance and radiation, electric
circuit effects. Homework (HW #2): No Homework. |
| Fri. Jan. 23, 2015 (WK2) |
Lecture: Propagation of waves in a waveguide: sinusoidal longitudinal
and time dependence. Splitting of the Maxwell equations into
longitudinal and transverse components. Homework (HW #2): No Homework. |
| Mon. Jan. 26, 2015 |
Lecture: Waveguide equations continued: the transverse fields in terms
of the longitudinal fields. TE, TM, and TEM waves. Homework (HW #3): No homework. |
| Wed. Jan. 28, 2015 |
Lecture: Solving waveguide problems: boundary conditions,
geometry. Non-existence of TEM waves in waveguides. Homework (HW #3): Jackson 8.4 (a). |
| Fri. Jan. 30, 2015 (WK3) |
Lecture: Waveguides concluded: a summary of how to solve for the modes
in a waveguide, which ones propagate, cylindrical waveguides,
cavities. The different approaches of Jackson and Griffiths to
radiation from sources. Approximations (with reasons) involving d, λ, and
r. Homework (HW #3): Jackson 8.6 (a). |
| Mon. Feb. 2, 2015 |
Lecture: The vector potential and the magnetic field due to a small
volume of oscillating charges / currents in the E1 approximation. Homework (HW #4): Jackson 9.5, with the following simplifications: Part (a): Work out only the scalar potential; the vector potential was done in class. Note: As discussed in Jackson at the end of section 9.1, the monopole term in the 1/distance expansion does not yield radiation. Instead, we must replace the exponential with -ik · x'(1 - 1/ikr), which results from using the expansion (9.12). Part (b): Work out only the electric field; the magnetic field was done in class. |
| Wed. Feb. 4, 2015 |
Lecture: Radiation fields for E1 radiation. The Poynting vector and
radiated power. Dependence of power on distance, direction, frequency;
polarization of the radiation. Homework (HW #4): No homework. |
| Fri. Feb. 6, 2015 (WK4) |
Lecture: Summary of E1, M1, E2 radiation: fields, differential power
(angular distribution) and total power. The Larmor formula for dipole radiation.
Examples of oscillating electric dipoles (two charges, two-wire dipole
antenna) and magnetic dipoles (loops, pulsars). The radiation resistance of antennas.
Homework (HW #4): Jackson 9.3. |
| Mon. Feb. 9, 2015 |
Lecture: E1 and M1 scattering of electromagnetic radiation by small
scatterers (size << wavelength). Homework (HW #5): Jackson 10.1 (a). |
| Wed. Feb. 11, 2015 |
Lecture: Rayleigh scattering, the blue sky, and polarization
asymmetry. Polarization of light scattered from the sky. Homework (HW #5): Jackson 10.1 parts (b) and (c). |
| Fri. Feb. 13, 2015 (WK5) |
Lecture: No Rayleigh scattering in the Martian sky, Reflection of rain
by radar, Huygens principle and single-slit diffraction. Homework (HW #5): No homework. |
| Mon. Feb. 16, 2015 |
Lecture: Relativity Quiz and discussion of the quiz. Dipole radiation
pattern and N-slit diffraction pattern. Homework (HW #6): No homework. |
| Wed. Feb. 18, 2015 |
Lecture: Derivation of the Huygens-Fresnel principle [Jackson's
equation 10.86] in the scalar approximation. Homework (HW #6): Consider a plane wave (wavenumber k) incident along the z direction and perpendicular to a large conducting screen with a small rectangular aperture whose (x, y) dimensions are (2a, 2b). Thus, we could say that x lies in the range [-a, a] and y in the range [-b, b]. A screen is placed a distance L downstream, and is also perpendicular to the z direction. Find an expression for the diffraction pattern (intensity distribution) on this screen assuming that the screen is far away (tens of cm or farther) and the aperture widths are at most a few wavelengths. |
| Fri. Feb. 20, 2015 (WK6) |
Lecture: Poisson's (or Arago's) Spot: derivation of the scalar wave on
axis. Homework (HW #6): Jackson 10.11 (a) and (b). |
| Mon. Feb. 23, 2015 |
Test #1: Everything covered up to Fri., Feb. 13: essentially all the
material we covered in Chapters 7, 8, 9, 10. Homework (HW #7): No homework. |
| Wed. Feb. 25, 2015 |
Lecture: A brief history of units in electromagnetic
theory. Introduction to Special Relativity: the Galilean
transformation and its impact on the electromagnetic wave
equation. Homework (HW #7): No homework. |
| Fri. Feb. 27, 2015 (WK7) |
Lecture: The principle of relativity as stated by Galileo. The Voigt
and Lorentz transformations. Invariance of the wave equation under
Lorentz transformations and constancy of the speed of light. Homework (HW #7): Jackson 11.1. |
| Mon. Mar. 2, 2015 |
Lecture: Review of Test 1. Homework (HW #8): No homework. |
| Wed. Mar. 4, 2015 |
Lecture: Test 1, take 2. Homework (HW #8): No homework. |
| Fri. Mar. 6, 2015 (WK8) |
Lecture: The coordinate 4-vector. Greek and Roman
indices and their meanings. Contra- and co-variant coordinate
4-vectors. Inner products of 4-vectors. The Lorentz transformation
matrix and its inverse. Arbitrary 4-vectors. A simple problem
involving length contraction and simultaneity. Homework (HW #8): Problems 3, 4 in the distributed "Relativity Problems". |
| Mon. Mar. 16, 2015 |
Lecture: The inverse and reverse Lorentz transformations, and how they
are the same thing. Lorentz invariance of inner product of two
4-vectors. Contra- and co-variant 4-vectors defined, and their Lorentz
transformations. Minkowski spacetime of special relativity and the
length of 4-vectors defined using the Minkowski metric. Transformation
of the gradient 4-vector. Homework (HW #9): No homework. |
| Wed. Mar. 18, 2015 |
Lecture: Invariance of the differential length squared leads to the
Minkowski metric being the same in all inertial frames. The rest
frame, instantaneous rest frame, and / or co-moving rest frame of a
particle. Proper time and time dilation. Spacetime diagrams.
Worldlines of particles. The light cone. Timelike and spacelike
intervals. Homework (HW #9): Jackson 11.3. |
| Fri. Mar. 20, 2015 (WK9) |
Lecture: Spacetime diagrams for the motion of four observers in two
different frames of reference: how the relative position of events on
the diagrams changes in a counter-intuitive way. Lengths of vectors on
spacetime diagrams and how the triangle inequality is not satisfied in
Minkowski geometry. Plots of hyperbolic functions. Rapidity. Homework (HW #9): Jackson 11.6. |
| Mon. Mar. 23, 2015 |
Lecture: Spacelike, lightlike, and timelike intervals. Four-velocity.
Four-momentum. Use of Lorentz invariants to solve kinematic problems.
First problem solved this way: the velocity addition formula. Homework (HW #10): No homework. |
| Wed. Mar. 25, 2015 |
Lecture: More 4-vector dot product applications: The Doppler Effect Formula.
The Compton Effect Formula. Homework (HW #10): Jackson 11.19. |
| Fri. Mar. 27, 2015 (WK10) |
Lecture: 4-vector dot product applications continued:
|
| Mon. Mar. 30, 2015 |
Lecture: The 4-current and the 4-potential. Casting the continuity
equation, the wave equation for the 4-potential, and the Lorenz
condition as relativistically covariant equations. The quotient
theorem. A relativistically fast run through a relativistically fast
falling rain. The attractive Lorentz force on a charge moving parallel
to and with speed identical to that of a linear current. A paradox:
the same charge appears to see no force in its rest frame and is not
attracted to the wire. Homework (HW #11): No homework. |
| Wed. Apr. 1, 2015 |
Lecture: Resolution of the paradox: transformation of the magnetic
field to an electric field. Definition of the electromagnetic field
tensor. Homework (HW #11): Jackson 11.27. |
| Fri. Apr. 3, 2015 (WK11) |
Lecture: More on the electromagnetic field tensor. Transformation of Electromagnetic Fields. Homework (HW #11): (a) Obtain the transformation in the form of Jackson's equation (11.149). (b) Read the rest of section 11.10 and obtain the remaining important equations for the fields of a moving charge on pages 559 and 560 [equations 11.151, 11.152, 11.153, 11.154, and the unnumbered equation between 11.152 and 11.153]. |
| Mon. Apr. 6, 2015 |
Report
by Suraj Poudel: Polarization by Double Refraction. Lecture: Gauge invariance and invariance of the antisymmetric electromagnetic field tensor in the Lorenz gauge. The inhomogeneous and homogeneous Maxwell equations. Lorentz transformations viewed as elements of a Lie group that can be generated by a continuous transformation. The infinitesimal generators must form an antisymmetric tensor. Homework (HW #12, due Apr. 17): Show that the Jacobi identity satisfied by the antisymmetric electromagnetic field tensor leads to the homogeneous Maxwell equations. |
| Wed. Apr. 8, 2015 |
Lecture: Proper and improper Lorentz transformations.
Generators of rotations and boosts. Homework (HW #12, due Apr. 17): Any one of Jackson 11.10 or 11.11. |
| Fri. Apr. 10, 2015 (WK12) |
Report by Francie Cashman:
Frequency Dispersion of Dielectric Gases. Report by Saba Arash: Center-Fed Antenna. Report by Alyssa Loos: Energy Gains and Losses in a RF Cavity. Lecture: Lorentz invariants formed from the field tensor. Rate of change of 4-momentum. The spin and momentum 4-vectors and how they behave differently under boosts. Homework (HW #12, due Apr. 17): Jackson 11.14. |
| Mon. Apr. 13, 2015 |
Report by Dheyaa Alameri:
Radiation Fields of a Linear Wire Antenna. Lecture: Thomas Precession. Homework (HW #13, due Apr. 22): Jackson 11.12. |
| Wed. Apr. 15, 2015 |
Test #2: Everything in the Special Relativity Chapter up until the
first half of the lecture on Monday, April 6. In other words,
essentially all of Jackson sections 1, 2, 3, 4, 5, 6, 9, 10 in Chapter 11. Homework (HW #13): No homework. |
| Fri. Apr. 17, 2015 (WK13) |
Report by Cory Dolbashian:
The Meissner Effect and the London Penetration Depth. Report by Sara Fitzgerald: Schumann Resonance. Lecture: Derivation of the BMT Equation and applications to special cases. Homework (HW #13, due Apr. 22): Thomas precession revisited: Starting from the BMT equation (11.164), derive equation (11.170). Unlike Jackson, you should not skip any steps (show all your work, with every step in detail). |
| Mon. Apr. 20, 2015 |
Lecture: Comparison of electron (or muon) momentum precession with
spin precession. The extra rate at which the spin precesses is shown
to be aγωc. The gyromagnetic anomaly as the
high-point of precision electrodynamics; muon (g-2) experiments.
Energy loss of charged particles in matter: the basic idea. Homework (HW #14, due Apr. 27): Jackson 12.12 (Jackson has some Chapter 11 problems at the end of Chapter 12 - possibly by mistake or because relativity got split into two chapters from a single chapter in some previous version of the text). |
| Wed. Apr. 22, 2015 |
Lecture: Energy loss of a charged particle per unit distance. Maximum
and minimum energy lost to a single electron. Homework (HW #14, due Apr. 27): Jackson 13.1. |
| Fri. Apr. 24, 2015 (WK14) |
Lecture: Course
review
for final exam. Homework (HW #14, due Apr. 27): No homework. |
| Mon. Apr. 27, 2015 |
Lecture: Preponed to Jan. 20, 2015. But HW #14 is still due today! Homework: No homework. |
| Wed. Apr 29, 2015 9:00 AM - 11:30 AM | FINAL EXAM: Covers ALL material! |