| Day, Date (Mon., dd, yyyy) | Lecture Content and Homework Assignment |
|---|---|
| Mon. Jan. 11, 2010 |
Lecture: Elementary discussion of waves. Homework (HW #1: due 1/20): Consider radiation from a standard 100W light bulb at the origin. You are standing 1 km from the bulb in the x-direction. Consider the 15% of the energy that goes into visible light and assume it is monochromatic at 6000 Angstroms. What is
|
| Wed. Jan. 13, 2010 |
Lecture: Orthogonality condition. Connection between magnetic and
electric fields. Inhomogenous waves. Plane and Circular Polarization. Homework (HW #1: due 1/20): Griffiths 9.33. |
| Thu. Jan. 14, 2010 |
Lecture: Griffiths problems 9.9, 9.11 Homework: None |
| Fri. Jan. 15, 2010 |
Lecture: Reflection and Refraction of Electromagnetic Waves. Refractive
indices. Homework (HW #2: due 1/25): Jackson 7.2. |
| Wed. Jan. 20, 2010 |
Lecture: Refractive index for dielectrics at low, medium and high
frequencies. Absorption. Conductivity. Homework (HW #2: due 1/25): Jackson 7.4. |
| Thu. Jan. 21, 2010 |
Lecture: Dispersion relation for plasmas and metals. Group and phase
velocity. Group velocity for electromagnetic waves. Homework (HW #2: due 1/25): Griffiths 9.23. |
| Fri. Jan. 22, 2010 |
Lecture: Introduction to Waveguides. Boundary conditions. Maxwell
equations applied to waveguides. Homework (HW #3: due 2/1): None. |
| Mon. Jan. 25, 2010 |
Lecture: Waveguides, continued. Homework (HW #3: due 2/1): Jackson 8.4a. |
| Wed. Jan. 27, 2010 |
Lecture: Waveguides, concluded. Homework (HW #3: due 2/1): Jackson 8.5a. |
| Fri. Jan. 29, 2010 |
Lecture: Oral exams: Chapters 7, 8. Homework (HW #4: due 2/8): Work out the electric and magnetic fields for TEM mode propagation in a cylindrical, coaxial conductor waveguide (Griffiths section 9.5.3). Also, solve Griffiths problem 9.31. |
| Mon. Feb. 1, 2010 |
Lecture: Conservation Laws: Griffiths Chapter 8. Homework (HW #4: due 2/8): Show that the Maxwell Stress Tensor is a tensor. |
| Wed. Feb. 3, 2010 |
Lecture: Energy and Momentum conservation for E.M. Fields. Examples of
the Poynting vector and the Maxwell Stress Tensor. Homework (HW #4: due 2/8): Griffiths 8.5. |
| Fri. Feb. 5, 2010 |
Lecture: Griffiths problem 8.4. Angular momentum in electromagnetic
Fields. Homework (HW #5: due 2/15): Griffiths 8.10. |
| Mon. Feb. 8, 2010 |
Lecture: Radiation from Radiating Systems. Homework (HW #5: due 2/15): "Simple Radiating Systems" (a) Prove the statement in the second sentence after Jackson eq. (9.8), where he says "It is easy to show that the fields ..." (b) Complete all the steps in the derivation of Jackson eq. (9.18) from eq. (9.13). |
| Wed. Feb. 10, 2010 |
Lecture: Electric Dipole Radiation and the Larmor Formula. Homework (HW #5: due 2/15): Jackson 9.7(a). Jackson 9.12 using P1 instead of P2. |
| Fri. Feb. 12, 2010 |
Lecture: Radiation from a Short, Center-fed Linear Antenna. Magnetic Dipole and Electric Quadrupole Radiation. Homework (HW #6: due 2/22): Jackson 9.15. |
| Mon. Feb. 15, 2010 |
Lecture: The elements of diffraction: diffraction from single, double
and multiple slits, and from a circular aperture. Fraunhofer vs
Fresnel diffraction. Homework (HW #6: due 2/22): Derive the N-slit diffraction formula. |
| Wed. Feb. 17, 2010 |
Lecture: Scalar Diffraction theory. Derivation of the Huygens-Fresnel
principle. Homework (HW #6: due 2/22): Jackson 10.11 a, b. |
| Fri. Feb. 19, 2010 |
Lecture: Babinet's principle of complementary screens. Example
problem: diffraction on axis of a circular aperture / disk. Homework (HW #7: due 3/1): "Rectangular Aperture". Work out the diffraction pattern when a plane wave is incident normal to a rectangular aperture and the Kirchoff approximation applies. |
| Mon. Feb. 22, 2010 |
Test 1: Covers all Jackson Chapters 7, 8, 9 and Griffiths Chapter 8
material that we studied until and including on Fri., Feb. 12. Homework (HW #7: due 3/1): None. |
| Wed. Feb. 24, 2010 |
Lecture: None (preponed - complete). Homework: None. |
| Fri. Feb. 26, 2010 |
Lecture: None (preponed - complete). Homework: None. |
| Mon. Mar. 1, 2010 |
Lecture: Gaussian units. See
Homework (HW #8: due 3/15): Jackson 11.1. |
| Wed. Mar. 3, 2010 |
Lecture: Invariance and Covariance revisited. Inertial reference
frames. Events. Inverse Lorentz transformation. Homework (HW #8: due 3/15): Show that the gradient of the potential in spherical coordinates equals that in Cartesian coordinates. |
| Fri. Mar. 5, 2010 |
Lecture: Invariant length of 4-vectors. Inner products (dot products)
of 4-vectors and their invariance. Rest Frames and Proper
time. 4-velocity, 4-momentum. The Doppler Effect. Homework (HW #9: due 3/22): Jackson 11.6. |
| Mon. Mar. 15, 2010 |
Lecture: Lorentz transformations in action: Length contraction and time dilation illustrated using
relativity problems. Homework (HW #9: due 3/22): Jackson 11.7. |
| Wed. Mar. 17, 2010 |
Lecture: General Lorentz Transformation. Time-like, Space-like and
Light-like intervals. Velocity addition formula. Covariant formulation of
laws. Non-relativistic limit of laws. Homework (HW #9: due 3/22): Jackson 11.3. |
| Fri. Mar. 19, 2010 |
Lecture: Transformation of coordinates of accelerating rockets. Homework (HW #10: due 3/29): Jackson 11.4. |
| Mon. Mar. 22, 2010 |
Lecture: Simple Lorentz transformation problems. Homework (HW #10: due 3/29): Griffiths, Elementary Particles, 3.5. |
| Wed. Mar. 24, 2010 |
Lecture: More relativstic energy-momentum problems. Homework (HW #10: due 3/29): Griffiths, Elementary Particles, 3.23, 3.24. |
| Fri. Mar. 26, 2010 |
Lecture: Contravariant and covariant 4-vectors. The metric
tensor. Higher rank tensors. Contraction of indices. Homework (HW #11: due 4/5): Consider the Cartesian and polar coordinates of position vectors in two dimensions. (a) Define xμ and its differential dxμ in both coordinate systems. (b) Find the (Lorentz-like) matrices which transform dxμ between the two frames. (c) Using the invariant interval ds² find also the metric tensor with both indices contravariant and with both indices covariant. (d) Find the covariant vector dxμ in polar coordinates. (e) Verify that ds² obtained from squaring dxμ is the same as ds² obtained from squaring dxμ. |
| Mon. Mar. 29, 2010 |
Lecture: Covariant formulation of electrodynamics: The contravariant
form of the 4-gradient, 4-force, transformation of forces, 4-current. Homework (HW #11: due 4/5): Griffiths (Electrodynamics) 5.19. |
| Wed. Mar. 31, 2010 |
Lecture: Covariant formulation of electrodynamics: The d'Alembertian,
4-potential, source equations in relativity, gauge conditions, the
antisymmetric electromagnetic rank-2 tensor Fμν.
Lorentz transformations of electric and magnetic fields. A paradox:
charge near a current-carrying wire. Relativistic run through the
rain. Homework (HW #11: due 4/5): Jackson 11.13. |
| Fri. Apr. 2, 2010 |
Lecture: Lorentz covariance of field equations. Brief review. Homework (HW #12: due 4/12): None. |
| Mon. Apr. 5, 2010 |
Test 2: Covers Diffraction and Relativity, including all material
covered in lectures up to and including Mar. 31. Homework (HW #12: due 4/12): Jackson 11.14. |
| Wed. Apr. 7, 2010 |
Lecture: The Dual tensor, Maxwell equations in covariant form, Lorentz
Force law in the extreme relativistic limit. 4-vector for Spin. Homework (HW #12: due 4/12): Jackson 11.17. |
| Fri. Apr. 9, 2010 |
Lecture: The spin 4-vector. The BMT equation. Homework (HW #13: due 4/19): None. |
| Mon. Apr. 12, 2010 |
Lecture: Muon spin precession. Homework (HW #13: due 4/19): Starting from the BMT equation (11.164), derive equations 11.170 and 11.171. Do not skip any steps (show all work). |
| Wed. Apr. 14, 2010 |
Lecture: Measuring (g-2) for muons. Thomas Precession. Homework (HW #13: due 4/19): Jackson 12.11. |
| Fri. Apr. 16, 2010 |
Lecture: Lagrangians for free particles and for particles in an
electromagnetic field. Homework (HW #14: due 4/26): Add the free field term mentioned at the end of class and, by considering variations of the Lagrangian with respect to the 4-potential, derive the field equations for the electromagnetic field. |
| Mon. Apr. 19, 2010 |
Lecture: Energy loss of charged particles in media: an introduction. Homework (HW #14: due 4/26): Jackson 11.26. |
| Wed. Apr. 21, 2010 |
Lecture: Energy loss, continued. Homework (HW #14: due 4/26): Derive the relation between the impact parameter |
| Fri. Apr. 23, 2010 |
Lecture: Dipole Radiation revisited. Radiation from an accelerating charge. Homework (HW #14: due 4/26): Derive the electric and magnetic fields of a moving charge, i.e., equations (14.13) and (14.14), from the 4-potential given as equation (14.8). [This approach, different from what Jackson does in section 14.1, is used by Griffiths in section 10.3.2.] |
| Mon. Apr. 26, 2010 |
Lecture: Relativistic generalization of the Larmor
formula. Application to particle accelerators. No Homework. |
| Tue. May 4, 2010 9:00 AM - 12:00 noon | FINAL EXAM: Covers ALL material! |