| Day, Date, Year | Lecture Content and Homework Assignment |
|---|---|
| Mon. Jan. 9, 2012 |
Lecture: Reminder of Maxwell's equations, plane waves. Introduction to
reflection and refraction at a boundary. Homework: None. |
| Tue. Jan. 10, 2012 |
Lecture (preponed): Reflection and refraction of a plane wave at a boundary. Homework #1 (due 1/18/12): Jackson 7.2. |
| Wed. Jan. 11, 2012 |
Lecture: Transmission and Reflection coefficients for waves incident
on a boundary. Model for ε(ω), anomalous dispersion and
resonant absorption. Homework #1 (due 1/18/12): Obtain the boundary conditions described by equations (7.40) and use them to deduce equations (7.41) and (7.42). |
| Fri. Jan. 13, 2012 |
Lecture: Numerical evaluation of (ε/ε0), showing that
air and most gases should be transparent at optical frequencies. High
frequency limit of (ε/ε0) and how the
resulting expression works also for metals and plasmas, i.e.,
attenuation / reflection at low frequncies followed by ultraviolet
transparency above the plasma frequency. Homework #1 (due 1/18/12): Jackson 7.13. |
| Tue. Jan. 17, 2012 |
Lecture (preponed): Imaginary refractive index. Simple model of
conductivity. Homework #2 (due 1/25/12): Jackson 7.12. |
| Wed. Jan. 18, 2012 |
Lecture: Waves, phase velocity, group velocity and application to
electromagnetic waves. Homework #2 (due 1/25/12): Jackson 7.20. |
| Fri. Jan. 20, 2012 |
Lecture: Waves in conductors. Characteristic time. Skin depth. Homework #2 (due 1/25/12): Jackson 8.1. |
| Mon. Jan. 23, 2012 |
Lecture: Introduction to waveguides: the Helmholtz equation and
recasting the Maxwell equations in terms of the transverse and
longitudinal fields for a wave in a waveguide. TE and TM modes
defined. The impossibility of TEM modes in a hollow waveguide. Homework #3 (due 2/1/12): Griffiths 9.27, 9.28. |
| Wed. Jan. 25, 2012 |
Lecture: Further discussion of waves in conductors. Solving for the
fields in a waveguide for TE and TM waves: equations, boundary
conditions and solutions. Homework #3 (due 2/1/12): Jackson 8.4a. |
| Fri. Jan. 27, 2012 |
Lecture: Fields in a waveguide, continued: expressions for TE and TM
waves. Power transmitted and power lost in a waveguide. Homework #3 (due 2/1/12): None. |
| Mon. Jan. 30, 2012 |
Lecture: Introduction to Radiation: Energy flow and energy density for
electric dipole radiation. The Larmor formula for radiation from an
accelerating charge. Homework #4 (due 2/8/12): Griffiths 11.21. |
| Wed. Feb. 1, 2012 |
Lecture: Derivation of radiation fields (far fields) in the E1 case. Homework #4 (due 2/8/12): Jackson 9.1. |
| Fri. Feb. 3, 2012 |
Lecture: Power transmitted by oscillating electric dipoles (E1
radiation). Resistance of practical dipole antennas. Homework #4 (due 2/8/12): Jackson 9.3 (4 points) and the following two questions about this problem (3 points each). Assume that the gap is equatorial. (a) What is the radiation resistance of this antenna? (b) If at time t=0 the hemisphere pierced by the positive z-axis has potential +V, what is the magnetic field B at (x, y, z) = (1, 2, 0.5) km and t=3.0s ? Assume that the frequency is 100 MHz, V=100 Volts and R=1m. Note that the speed of light c is known to be exactly 299792458 m/s, because the meter is defined in terms of c. |
| Mon. Feb. 6, 2012 |
Class Test #1 covers Chapters 7, 8. Homework #5 (due 2/15/12): None. |
| Wed. Feb. 8, 2012 |
Lecture: From electric dipole radiation (E1) on to M1 and E2 radiation
formulas. The Maxwell Stress Tensor. Force per unit volume on a
collection of charges. Homework #5 (due 2/15/12): Jackson 9.5. |
| Fri. Feb. 10, 2012 |
Lecture: Interpretation of momentum conservation using the Maxwell
Stress tensor. Momentum and angular momentum in the electromagnetic
field. Interpretation of the components of T as pressures and shear
pressures. Homework #5 (due 2/15/12): Griffiths 8.3, 8.10. |
| Mon. Feb. 13, 2012 |
Lecture: Summary of electromagnetic scattering by individual
scatterers. Homework #6 (due 2/22/12): Jackson 10.1. |
| Wed. Feb. 15, 2012 |
Lecture: Different units in E&M: SI, esu, emu, Gaussian, and rationalized
units. Invariance and Covariance: important concepts and a couple of
simple examples. Investigation of the covariance of the wave equation
under Galilean transformations. Homework #6 (due 2/22/12): Jackson 11.1. |
| Fri. Feb. 17, 2012 |
Lecture: Fitzgerald, Lorentz and Voigt. The Voigt transformation. The
Lorentz Transformation. 4-vectors. Frames of
Reference. Events. Invariant square of the position 4-vector. Homework #6 (due 2/22/12): Jackson 11.3. |
| Mon. Feb. 20, 2012 |
Lecture: Lorentz transformations along arbitrary directions.
Dot products of 4-vectors; invariance of dot products of
4-vectors. Proper time. 4-velocity. Length Contraction. Time
dilation. Homework #7 (due 2/29/12): Jackson 11.4. |
| Wed. Feb. 22, 2012 |
Lecture: Light cones. World Lines. Future. Past. Elsewhere. Intervals:
Time-like, Space-like, and Light-like. Using Lorentz invariant dot
products: Doppler Effect and Velocity Addition Formulas. Simple
relativity problems. Homework #7 (due 2/29/12): Griffiths 12.4, 12.7. |
| Fri. Feb. 24, 2012 |
Lecture: More relativity problems, including the twin paradox. Homework #7 (due 2/29/12): Jackson 11.6. |
| Mon. Feb. 27, 2012 |
Class
Test #2 covers Chapters 9, 10, 11 (sections 1 through 4) Homework #8 (due 3/14/12): None. |
| Wed. Feb. 29, 2012 |
Lecture: Continued discussion of elementary special
relativity. Energy-momentum 4-vector. The invariance of
mass. Energy-momentum conservation. Homework #8 (due 3/14/12): Griffiths Particle Physics 3.10, 3.11, 3.12. |
| Fri. Mar. 2, 2012 |
Lecture: Discussion of Griffiths's problems 12.1-12.15, with emphasis
on problems 12.10, 12.11, 12.14, 12.15. Homework #8 (due 3/14/12): Griffiths problem 12.11. |
| Mon. Mar. 12, 2012 |
Lecture: A bit of history: Galileo's Ship and the Principle of
Relativity. The triangle inequality, unexpected tilting of the plane
of simultaneity and other peculiar behavior in Minkowski
space. Contravariant and co-variant indices. The metric tensor. Homework #9 (due 3/21/12): Griffiths 12.26, 12.27. |
| Wed. Mar. 14, 2012 |
Lecture: Transformations of contra- and co-variant vectors. Two
kinematic problems: (1) Mandelstam variables for elastic scattering
and (2) Wavelength shift for Compton scattering. Homework #9 (due 3/21/12): Griffiths Particle Physics 3.13, 3.16, and parts (a) and (b) of 3.17. |
| Fri. Mar. 16, 2012 |
Lecture: Rapidity. Raising and lowering of indices. The derivative
4-vector and the d'Alembertian. Electromagnetic current
density. Examples. Wave equations in tensor form. The 4-potential. Homework #9 (due 3/21/12): (a) Consider a particle in motion and evaluate aμvμ where aμ is the acceleration 4-vector. (b) Write down the continuity equation (conservation of electric charge) in covariant form. |
| Mon. Mar. 19, 2012 |
Lecture: The ELectromagnetic Field Tensor Fμν. The
nature of transformations that leave lengths invariant in Minkowski
spacetime and the generators of proper Lorentz transformations. Homework #10 (due 3/28/12): (a) Prove Jackson's commutation relations (11.99). (b) Jackson 11.10. |
| Wed. Mar. 21, 2012 |
Lecture: Gauge invariance of the Field Tensor and gauge freedom in the
4-potential. The Lorentz Force Law in relativistic notation. Homework #10 (due 3/28/12): Jackson 11.14. |
| Fri. Mar. 23, 2012 |
Lecture: Lorentz transformations of electric and magnetic field
components using the antisymmetric field tensor. The fields of a
moving charge and a moving magnet. Homework #10 (due 3/28/12): Jackson 11.15. |
| Mon. Mar. 26, 2012 |
Lecture: Spin and Thomas Precession in the 1920's. The g-factor. The
spin 4-vector and an introduction to the BMT equation. Homework #11 (due 4/4/12): Jackson 11.11, 11.12. |
| Wed. Mar. 28, 2012 |
Lecture: The BMT equation. Homework #11 (due 4/4/12): Starting from the BMT equation (11.164), derive equations 11.170 and 11.171. Unlike Jackson, you should not skip any steps (show all your work, with every step in detail). |
| Fri. Mar. 30, 2012 |
Lecture: Applications of the BMT equation: Muon spin precession and
Thomas precession, revisited. Homework #11 (due 4/4/12): Jackson 12.11. |
| Mon. Apr. 2, 2012 |
Class
Test #3 covers Special Relativity, Jackson's Chapter 11 except
for the spin-related sections: 11.8 and 11.11. No Homework. |
| Wed. Apr. 4, 2012 |
Lecture: Towards an action principle description of charged particles
and electromagnetic fields. Homework #12 (due Monday, 4/9/12): Write down a non-relativistic Lagrangian for a charged particle in an electromagnetic field and derive the Lorentz Force law from the Lagrangian. |
| Fri. Apr. 6, 2012 |
Lecture: Including the interaction term in the Lagrangian. Homework #12 (due Monday, 4/9/12): None. |
| Mon. Apr. 9, 2012 |
Lecture: Including the electromagnetic field terms in the Lagrangian. Homework #13 (due 4/18/12): Jackson 12.2. |
| Wed. Apr. 11, 2012 |
Lecture: Preponed to Jan. 10, 2012. Homework #13 (due 4/18/12): None. |
| Fri. Apr. 13, 2012 |
Lecture: Preponed to Jan. 17, 2012. Homework #13 (due 4/18/12): None. |
| Mon. Apr. 16, 2012 |
Lecture: Two relativistic kinematics problems. Homework #14 (due 4/23/12): None. |
| Wed. Apr. 18, 2012 |
Lecture: Discussion of more relativistic kinematics problems, derived from the A to
C exam. Homework #14 (due 4/23/12): Jackson 11.26. |
| Fri. Apr. 20, 2012 |
Lecture: Brief description of energy loss of charged particles in
matter. Homework #14 (due 4/23/12): No homework. |
| Mon. Apr. 23, 2012 |
Lecture: Review of course. Homework: None. |
| Sat. Apr 28, 2012 9:00 AM - 12:00 noon | FINAL EXAM: Covers ALL material! |