Physics 210A is available here.
Announcements:The Final Exam is now available.
Douglas M. Eardley
<doug@kitp.ucsb.edu> (the best way to reach me)
Phone: -2280, Fax: -2431
Office hours this week are 2:30-4pm Thursday, Room 2329 KITP (Kohn Hall). If you
want to meet me at another time, email or call first to make an appointment.
TA: Hieu Nguyen <doubleslash@gmail.com>, office hours 11:30-1:00 Tue, 12:30-2:00 Fri..
Course Web Page (this page):
It will be updated steadily as the course goes on, so please visit it frequently.
This class is the second quarter of a 2-quarter introductory course on classical electrodynamics at the graduate level. The entire course will cover these important topics: Electrostatics, magnetostatics, boundary value problems, time varying fields, Maxwell's equations, radiation, multipole fields, scattering, and relativistic particle dynamics.
The required text for the entire course is Classical Electrodynamics (3rd Ed, 1998), by John David Jackson (John Wiley & Sons; ISBN: 0-471-30932-X), available through (e.g.) www.amazon.com, www.wiley.com, or in the UCSB bookstore. We will cover the first half of the book winter quarter.
| Week of | Topic | Chapter |
|---|---|---|
| Mar 31 | Plasma waves, dispersion | 7,8 |
| Apr 7 | Waveguides and cavities | 8 |
| Apr 14 | Radiation and multipoles | 9 |
| Apr 21 | Scattering and diffraction | 10 |
| Apr 28 | Relativity theory | 11 |
| May 5 | Midterm exam | |
| May 12 | Dynamics of particles and fields | 12 |
| May 19 | Radiation by moving charges | 13 |
| May 26 | Radiation by moving charges | 14 |
| Jun 2 | Radiative processes | 15,16 |
| Final exam |
Dates may vary, please check this webpage often for the latest information.
Course grading will be tentatively 60% homework, 30% final, 10% midterm. The midterm and final exams will be open-book, take-home exams.
Homework will be due Wednesdays in TA Hieu Nguyen's mailbox in Room 5340 Broida Hall (the palatial Graduate Lounge), by 4:30pm. Homework 1 will be due Tuesday, Apr 8. Late homework will be accepted only at the convenience of the TA; please get approval beforehand from the TA or professor. Solutions will be posted later.
Reading: Jackson Chapter 7; begin Chapter 8.
No Homework this week.
Reading: Jackson Chapter 8.
Homework set 1: Due Tuesday Apr 8. Jackson Chapter 7 (pp340ff): problems 7.3 (for perpendicular polarization only), 7.18, 7.19, 7.22. Solutions 1 are available here.
Hint on Problem 7.18: Try working in Fourier space (of ω and vector wavenumber k);
arrange the equations of motion (7.75) into the form Mv = ω2v,
where M is a 3x3 matrix composed
of components of k and constants; and where v is the 3-vector fluid velocity.
For instance, a term like (k.v)k, when written out in components, is the same as a
matrix (kikj) times a vector v_j. Then you have what
is just an eigenvalue problem; for given k, you need to find the eigenfrequencies ω
that allow a solution. Then, you can find the corresponding eigenvectors v.
Explanation of
Problem 7.19: The mean position <x> of the pulse is defined by
<x> = integral dx x |u|2 / integral dx |u|2
and mean square deviation from the mean is defined by
<Delta x>2 = integral dx (x2 - <x>2) |u|2 / integral dx |u|2
The rms deviation is just the square root of the latter. These
are just instances of the usual formulas for the mean and variance
of a distribution. Similar formulas hold in k-space for A(k).
Reading: Jackson Chapter 9. No class Tue Apr 15.
Homework set 2: Due Tuesday Apr 15. Jackson Chapter 8 (pages 396ff):
8.2abc*, 8.4a^, 8.5a#, 8.6a^, 8.15a+.
Solutions 2 are available here.
Explanations:
*Problem 8.2: Part 8.2d) will be considered extra credit, because
it takes us far into the details.
^Problems 8.4, 8.6:Do only part a).
#Problem 8.5: Do only part a). One simple approach is to
imagine a square waveguide of side a, as big as two of our triangles
butted together. You know all of the modes for the square waveguide;
just pick the modes which in addition obey the proper boundary condition
along the hypotenuse; these will be either even or odd under reflection
through the hypotenuse. (You may need linear combinations of degenerate
modes from the square.)
+Problem 8.15: Do only part a) and only for TE modes. Hint: Find
a solution which is a sum of two plane waves inside the slab, and two evanescent
waves outside. This problem is the flip side of Problem 7.3, which you have
already done. It is yet another eigenvalue problem: You get a system
of 4 linear equations relating the 4 wave amplitudes E_i (but if you are
clever you can reduce it to 2 equations).
For any old k you would not expect to find a solution for
the E's. but for certain k you will get a solution, if
the determinant of the matrix multiplying the E's vanishes.
See further details.
Reading: Jackson Chapter 10.
Homework set 3: Due Tuesday Apr 22. Jackson Chapter 9 (pages 449ff): 9.3, 9.5, 9.11, 9.14, 9.16a. Solutions 3 are available here.
Discussion of Problems 3 and 5 in Chapter 9: Both these problems address electric
dipole radiation, the lowest-order radiative pattern. In Problem 9.3, you can first solve the
problem as a quasi-electrostatic problem, determine the electric dipole component
of the exterior potential, and then apply Eqs. (9.19, 9.23, 9.24).
In Problem 9.5, you are to make the lowest-order approximation in source position
x', in the far-field formulas for the potentials (Eq. 9.2, and the top equation on p.410).
The latter equation features the one tricky part: the 0th order term in x' vanishes
for the scalar potential, due to conservation of charge, so the lowest contributing term is 1st order.
Jackson's argument is perhaps confusing on this point. We can frame the argument as follows: Given a charge density and current density which are functions of (x',t). Due to conservation of charge, the spatial integral q(t) of the charge density is independent of time, q(t)=qo. We next Fourier transform to frequency ω in place of time t, so our transformed densities and fields are all functions of (x',ω); in the book the ω-dependence is, confusingly, suppressed. Therefore, the Fourier transform q(ω) of the spatial integral of the charge density vanishes except at ω=0, where it is proportional to a delta-function δ(ω). Accordingly, the formula for the Fourier transform Φ(x',ω) of the scalar potential has a vanishing 0th-order term in the x'-expansion; except for a possible delta-function at ω=0.
Reading: Jackson Chapters 10, 11.
Homework set 4: Due Wed Apr 30. Jackson Chapter 10, pages 507ff, 10.1, 10.9, 10.12. Solutions 4 are available here.
Hint on Problem 10.9b: The Born-approximation integral over the sphere can be set up in spherical coordinates. The integrals over r and φ can be done straightforwardly, leaving a messy integral over θ, in which the variable of integration can be changed to qa. At this point you probably need to consult a table of integrals, or Mathematica.
The take-home midterm is here. And the solutions are here.
Reading: Jackson Chapters 11, 12.
No homework this week. Takehome midterm due (in TA's mailbox) 4:30pm Wed May 7.
Reading: Jackson Chapters 12.
Homework set 5: Due Wed May 14. Jackson Chapter 11, pages 568ff, 11.3, 11.4, 11.13, 11.15. Jackson Chapter 12, pages 617ff, 12.3. Solutions 5 are available here.
Puzzle: Here is the puzzle announced in class on May 15: Pretend we know all about nonrelativistic electrostatics (unlike charges attract, like charges repel, inverse square law, conservation of charge) but nothing about magnetism. If we also knew special relativity, what relativistic theory of electricity would we invent? Could it just be a scalar theory, generalizing the electrostatic potential? Or would we be forced to invent the field tensor, and thereby predict the existence of magnetic effects? Why or why not? I will give an answer (or actually several) on Tuesday; see what answers you can come up with. (This is not homework, nothing to turn in.)
This puzzle is not totally silly, because in 1905, we were in exactly the same position with regard to gravity. We knew "gravitostatics" in the nonrelativistic limit, and we (or rather Einstein) had just invented special relativity.
Reading: Jackson Chapters 13.
Homework set 6: Due Wed May 21. Jackson Chapter 12, pages 617ff, 12.1a (omit part b), 12.5, 12.6, 12.9abc (omit part d), 12.14. Solutions 6 are available here.
Reading: Jackson Chapter 14.
Homework set 7: Due Wed May 28. Jackson Chapter 13, pages 655ff: 13.2, 13.4, 13.9. Solutions 7 are available here.
Reading: Jackson Chapters 14, 15.
Homework set 8 (last): Due Wed June 4. Jackson Chapter 14, pages 698ff, 14.4, 14.11, 14.12.
No class Tue June 3.
Last regular class meeting: Thu June 5.
24 hr take-home final begins noon Tue June 10.
Available online here.
Due noon Wed June 11 in the TA's mailbox.
The exam is open-book, and will cover Chapters 8-14, along with the
basic ideas of Chapter 15.
dme 06/10/08