| Day, Date, Year | Lecture Content and Homework Assignment |
|---|---|
| Mon. Jan. 14, 2013 |
Lecture: Introduction to electromagnetic waves. Homework #1 (due 1/23/13): Consider radiation from a standard 100W light bulb at the origin. You are standing 1 km from the bulb in the x-direction. Consider only the 15% of the energy that goes into visible light (ignore the rest) for all of the following, and assume it is monochromatic at 6000 Angstroms and flowing outwards as a coherent spherical wave. What is
|
| Wed. Jan. 16, 2013 |
Lecture: The wave equation and its solution: for strings! Homework #1 (due 1/23/13): Griffiths 9.9. |
| Fri. Jan. 18, 2013 |
Lecture: A detailed description of plane and circularly polarized
electromagnetic waves. Homework #1 (due 1/23/13): Work out the transmission and reflection coefficients for a stretched string with tension T at a boundary where the linear mass density λ changes abruptly from region 1 (left) to region 2 (right). Assume that a transverse wave is incident from the left, and has angular frequency ω. |
| Tue. Jan. 22, 2013 |
Lecture (preponed): Reflection and Transmission of electromagnetic waves at a
dielectric boundary: part I. Homework #2 (due 1/30/13): Jackson 7.2. |
| Wed. Jan. 23, 2013 |
Lecture: Reflection and Transmission: part II. Transmission and Reflection coefficients for waves incident
on a boundary. Model for ε, anomalous dispersion and resonant
absorption. Homework #2 (due 1/30/13): Obtain the boundary conditions described by equations (7.40) and use them to deduce equations (7.41) and (7.42). |
| Fri. Jan. 25, 2013 |
Lecture: Interpretation of expression for ε(ω) as a
function of frequency for metals and plasmas. Connection to
conductivity. Homework #2 (due 1/30/13): Jackson 7.13. |
| Mon. Jan. 28, 2013 |
Lecture: Propagation of groups of waves: Fourier transforms of wave
packets, phase and group velocity. Phase and group velocity in the
normal and anomalous regions and for metals and plasmas. Homework #3 (due 2/6/13): Jackson 7.20. |
| Wed. Jan. 30, 2013 |
Lecture: Waves in conductors: characteristic time and skin depth. Homework #3 (due 2/6/13): Griffiths 9.19. |
| Fri. Feb. 1, 2013 |
Lecture: Waveguides: the Maxwell Equations split into transverse and
longitudinal equations. The wave equation converted to a
2-dimensional Helmholtz equation. Homework #3 (due 2/6/13): None. |
| Mon. Feb. 4, 2013 |
Lecture: Solving waveguide equations, part I. Homework #4 (due 2/13/13): TEM Waves: Just before equation (8.27) Jackson states that "There are three main consequences." State and prove these three consequences. |
| Wed. Feb. 6, 2013 |
Lecture: Waveguides, part II. ppt presentation. Waveguide theory applied to rectangular cross-section
waveguides. TE and TM modes, cutoff frequencies, electric and
magnetic field components.
Homework #4 (due 2/13/13): Jackson 8.4a. |
| Fri. Feb. 8, 2013 |
Lecture: Introduction to radiation: How to use the Larmor formula to solve
simple problems. Homework #4 (due 2/13/13): Griffiths 11.9. |
| Mon. Feb. 11, 2013 |
Lecture: Radiation from oscillating current sources. The dipole approximation. Homework #5 (due 2/20/13): Jackson 9.3. |
| Wed. Feb. 13, 2013 |
Test #1
on everything we've covered from Jackson Chapters 7, 8, i.e.,
all material in the course up to and including the lecture on 2/6/13. Homework #5 (due 2/20/13): No Homework. |
| Fri. Feb. 15, 2013 |
Lecture: Radiation Fields for the Electric Dipole (E1) case. Homework #5 (due 2/20/13): Derive the fields (eq. (9.18)) from the vector potential (eq. (9.16)) using the usual expressions (eqs. (9.4) and (9.5)). |
| Mon. Feb. 18, 2013 |
Lecture: Differential and total power radiated for E1
fields. Radiation fields for the E1, M1, and E2 cases and
expressions for radiated power. Homework #6 (due 2/27/13): Jackson 9.5. Note that here Jackson is not asking for radiation fields, so the simplest approximation for the potentials will not work. You have to include a bit more, and the discussion preceding eqs. (9.11) and (9.12) should help. |
| Wed. Feb. 20, 2013 |
Lecture: Solving problems: the dipole antenna, Jackson 9.5, 9.12, 9.13, 9.14, 9.16. Homework #6 (due 2/27/13): Pulsar problem |
| Fri. Feb. 22, 2013 |
Lecture: Distinguishing radiation problems as E1, M1, E2. Chief
characteristics: dependence on frequency, moment,
angle. Scattering. Why the sky is blue. Polarization of radiation
scattered by the sky. Homework #6 (due 2/27/13): Jackson 9.2. |
| Mon. Feb. 25, 2013 |
Lecture: Further discussion of scattering of light by small dielectric
spheres. Homework #7 (due 3/6/13): Derive Jackson's eqs. (10.3), (10.4), and (10.6). You may assume that no magnetic dipole moment m is induced by the incident electromagnetic field. |
| Wed. Feb. 27, 2013 |
Lecture: Units in electromagnetic theory. Invariance and
Covariance. Example of covariance. The wave equation. Galilean
transformations. Homework #7 (due 3/6/13): None. |
| Fri. Mar. 1, 2013 |
Lecture: The wave equation under Galilean, Voigt, and Lorentz
transformations. Introduction to 4-vectors. Homework #7 (due 3/6/13): Jackson 11.1. |
| Mon. Mar. 4, 2013 |
Lecture: Lorentz transformations and 4-vectors. Examples of
4-vectors. The "length-squared" of a 4-vector is invariant under a
Lorentz transformation. Homework #8 (due 3/20/13): Show that the dot product of two 4-vectors is invariant under a Lorentz transformation. |
| Wed. Mar. 6, 2013 |
Lecture: Proper time and its invariance. The velocity and
energy-momentum 4-vectors. Energy is a function of velocity, mass is
not! Energy as the sum of rest energy and Kinetic Energy =
mv2/2 for v << c. Homework #8 (due 3/20/13): Jackson 11.3. |
| Fri. Mar. 8, 2013 |
Lecture: Spacetime diagrams. Light cones (null cones). The geometry of
Minkowski spacetime is weird: longer-looking lines have shorter
lengths! [This explains the twin paradox.]
Energy-momentum conservation problems solved using 4-vectors
and Lorentz-invariant dot products. Example: Derivation of the Compton
scattering formula for the wavelength increase as a function of
scattering angle. Homework #8 (due 3/20/13): Jackson 11.19. |
| Mon. Mar. 18, 2013 |
Lecture: Spacetime: Minkowski's quote from 1908. Curves of constant distance from
the origin within the light cone. Relativistic kinematics
problems: (a) energy of a decay product in two-body decays, (b) minimum beam
energy required to produce a given final state. Homework #9 (due 3/27/13): Jackson 11.20. |
| Wed. Mar. 20, 2013 |
Lecture: Length contraction and time dilation using Lorentz
transformations. Using Lorentz invariants: Doppler effect, velocity
addition calculated using invariants. Review for the test on Friday. Homework #9 (due 3/27/13): Jackson 11.4. |
| Fri. Mar. 22, 2013 |
Test #2
on everything we've covered from Jackson Chapters 9, 10, and
parts of 11, i.e., all material in the course from the lecture on
2/8/13 up to and including the lecture on 3/8/13. Homework #9 (due 3/27/13): Jackson 11.6. |
| Mon. Mar. 25, 2013 |
Lecture: Transformations of the coordinate 4-vector and its
derivatives (the 4-gradient): definition of the contra- and co-variant
forms of 4-vectors. The metric tensor and its form for Minkowski
spacetime. Tensors with more than one index: higher rank tensors and
how they transform. Homework #10 (due 4/3/13): Jackson 11.9. |
| Wed. Mar. 27, 2013 |
Lecture: Recap of last lecture. Contra- and co-variant forms of the
coordinate 4-vector. Two important features of the metric tensor:
defining lengths (providing a metric!) and raising and lowering
indices, i.e., converting contravariant indices to covariant ones and
vice-versa. The current and potential
4-vectors. The continuity equation cast in covariant form. The source
equations for potentials cast in covariant form. Gauge invariance in
relativistic notation: the d'Alembertian of the added gradient of a
scalar function must vanish. Homework #10 (due 4/3/13): Jackson 11.22. |
| Fri. Mar. 29, 2013 |
Lecture: The Lorentz group; proper and improper Lorentz
transformations. Conditions on Lorentz transformation
matrices. Generators of boosts and rotations. Rapidity. Commutation
relations for generators. Homework #10 (due 4/3/13): Jackson 11.10. |
| Mon. Apr. 1, 2013 |
Lecture: Lorentz tranformations of the 4-current density: relativistic
rain and charge travelling parallel to a wire. Introduction to and
gauge invariance of the electromagnetic
rank-2 antisymmetric field tensor Fμν. Homework #11 (due 4/10/13): Jackson 11.11. |
| Wed. Apr. 3, 2013 |
Lecture: None - Preponed to 1/22/2013. Homework #11 (due 4/10/13): None. |
| Fri. Apr. 5, 2013 |
Lecture: The field tensor Fμν and Lorentz transformations of
electric and magnetic fields. Homework #11 (due 4/10/13): Jackson 11.13. |
| Mon. Apr. 8, 2013 |
Lecture: The dual tensor. Casting the Maxwell Equations and the
Lorentz Force Law in covariant form. Homework #12 (due 4/17/13): Jackson 11.14 parts (a) and (b) only. |
| Tue. Apr. 9, 2013 |
Lecture: Student presentations (see table at the bottom of this page) in the Rogers Room starting at 1:00 PM. Homework #12 (due 4/17/13): None. |
| Wed. Apr. 10, 2013 |
Lecture: Thomas Precession. Homework #12 (due 4/17/13): Work out details of the boosts involved in Thomas Precession, i.e., obtain Jackson's equations (11.116) and (11.117) from (11.112) by working out all the intermediate steps in detail. |
| Fri. Apr. 12, 2013 |
Lecture: Spin precession in relativity. Student presentations (see
table at the bottom of this page). Homework #12 (due 4/17/13): Jackson 11.16. Hint: For part (a), consider first what the given expression is in the rest frame of the conducting medium. |
| Mon. Apr. 15, 2013 |
Lecture: Spin precession: comparison of momentum and spin. The BMT
equation. Muon spin precession. Student presentations (see table at
the bottom of this page). Homework #13 (due 4/24/13): 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). |
| Wed. Apr. 17, 2013 |
Lecture: Comments on the 3-dimensional Thomas precession expressions
and the BMT equation. Student presentations (see table at the bottom of this page). Homework #13 (due 4/24/13): Muon spin precession revisited: Starting from preceding equations, derive equation 11.171. Unlike Jackson, you should not skip any steps (show all your work, with every step in detail). |
| Fri. Apr. 19, 2013 |
Lecture: Lagrangians for free particles. Homework #13 (due 4/24/13): None. |
| Mon. Apr. 22, 2013 |
Lecture: The Euler-Lagrange equations from the Principle of Least
Action. Homework #14 (due 4/29/13): Jackson 12.1. |
| Wed. Apr. 24, 2013 |
Lecture: Motion of a charged particle in electromagnetic fields: (a)
in a uniform magnetic field, (b) in crossed uniform electric and
magnetic fields. Homework #14 (due 4/29/13): Jackson 12.5. |
| Fri. Apr. 26, 2013 |
Lecture: None - Preponed to 4/9/2013. Homework #14 (due 4/29/13): None. |
| Mon. Apr. 29, 2013 |
Lecture: Review of all course material. Homework: None. |
| Sat. May 4, 2013 9:00 AM - 11:30 AM | FINAL EXAM: Covers ALL material! |
| Student | Presentation Topic |
|---|---|
| Sean Morrison | Resolving Power of Diffraction Gratings Slides Report |
| Jia Zhao | Physics of the Microwave Oven Slides Report |
| Colin Gleason | Synchrotron Radiation From Insertion Devices Slides Report |
| Nahid Shayesteh | Q of a Cavity Slides |
| Katia Gasperi | Dispersion in Dielectrics Slides |
| Iuliia Skorodumina | Energy flow and attenuation in waveguides Slides |
| Bing Guo | The Abraham-Lorentz Force Slides |
| Saptaparnee Chaudhuri | Propagation of EM waves in the Ionosphere Slides |