Electromagnetic Field Theory II

Physics 835, Winter 2009

Welcome to the Physics 835 home page! The course information is available here plus lots of supplementary info. Please check this page regularly.

Office: M2046 Physics Research Building (PRB)

Office Hours: Mondays, Tuesdays, 11:00 am - 12:00 pm

Course Meets: Mondays, Wednesdays 8:30 am - 10:18 am, Smith 1180. (Exceptions will be announced in class and posted here.)

Grader: Ke Li (office: PRB 1112; phone: 247-8226; email: li.744@osu.edu)

Recent additions to this page:

*** The final exam will take place on Monday, March 16, 2009, 8:00-10:30am in PRB 1080 (Physics Research Building) ***
*** Bring paper, pencil, and eraser. This is a closed book exam. You may bring 2 letter-size sheets of handwritten notes ("cheat sheets"). ***
*** Most potentially useful formulae will be given in the problem statements for the exam. ***

*** By popular demand, the homework due date has been shifted to Thursdays (instead of Wednesdays). This gives you an extra day (assignments are still announced the Wednesday before), but it eliminates any possibility of submitting homework late. No homework will be accepted after 11:59pm on the due date (Thursday)! ***

Topics:

• Maxwell Equations, Green Functions for Wave Equation, Poynting Vector, Maxwell Stress Tensor, Magnetic Monopoles
• Electromagnetic Waves and their Propagation
• Waveguides and Cavities
• Radiation, Multipole Expansion
• Scattering and Diffraction, Optical Theorem (if time permits)

Textbook:

• J. D. Jackson - Classical Electrodynamics, 3rd Edition

Recommended Reading :

• L.D. Landau, E.M. Lifshitz - The Classical Theory of Fields: Volume 2
• L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii - Electrodynamics of Continuous Media: Volume 8
• D.J. Griffiths - Introduction to Electrodynamics (this is a useful book to refresh your memory, but it does not cover all the material we will discuss in class)
• Hans C. Ohanian - Classical Electrodynamics, 2nd Edition (this has nice introductory chapters and practice problems on vector calculus and special relativity, but it uses CGS units, so you must correct for this when comparing Ohanian's way of dealing with the subject with Jackson's)

Lecture Notes:

• Chapter 6: Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws
  • Lecture 1 (1/5/09)
• Lecture 2 (1/7/09)
• Chapter 7: Plane Electromagnetic Waves and Wave Propagation
  • Lecture 3 (1/12/09)
  I have included two pages of notes on magnetic monopoles
  and the Dirac quantization condition even though I didn't cover this in class.
• Lecture 4 (1/14/09)
• Lecture 5 (1/21/09)
• Midterm review pages from Prof. Yuri Kovchegov's course (1/21/09) (ignore the last page on wavr guides)
• Lecture 6 (1/26/09)
• Lecture 7 (2/9/09)
• Chapter 9: Radiating Systems, Multipole Fields and Radiation
  • Lecture 8 (2/11/09)
• Lecture 9 (2/16/09)
• Lecture 10 (2/18/09)
• Lecture 11 (2/23/09)
• Lecture 12 (2/25/09)
• Chapter 10: Scattering
  • Lecture 13 (3/2/09)
• Lecture 14 (3/4/09)
• Lecture 15 (3/9/09)
• Final exam review sheets (3/10/09)

Homework Assignments:

Homeworks are due at 11:59 pm on the due date. Please put them in the grader's mailbox in PRB or slide them under his office door if the main office is already closed. Late submissions are not possible.
(Solutions are password protected, they are for the use of OSU students and faculty only, please write to me if you belong to that group and are interested in accessing them.)
Each problem is worth 10 pts unless stated otherwise.

• HW 1 (due Wednesday, January 14, 2009) Jackson Problems 6.1, 6.4 (20 points for this one!), 6.9, and 6.10.
  Hints for Problem 6.4: (a) Try to find a way to make use of Eqs. (5.159), (5.142) and (5.105) in the text
  (b) For a hint what kind of symmetry argument could be made see Lecture 13 from last quarter.
  (c) From parts (a) and (b) you should be able to calculate the electric field in- and outside the rotating sphere. How does this give you access to a possible surface charge density? Check that the surface charge density compensates exactly the volume charge density in part (a) so that your rotating sphere remains overall neutral!
  (d) Why is the electromotive force from the equator to the pole independent of the path? Use this to find an "easy" path to do your calculation. -- Solution 1
• HW 2 (deadline extended by popular demand to Thursday, Jan. 22, 2009, 11:58pm) Jackson Problems 7.2 (20 pts.), 7.4 (15 pts.), 7.5 (10 pts.), and 7.6 (part (a) only, 5 pts.)) (50 pts. total)
  Hints: Problems 7.2 and 7.4: Note the word "non-permeable"!
  Problem 7.4(b): Note that Jackson defines in (5.165) the skin depth by a factor differently from what we used in class!
  Problem 7.5: Use the similarities of this problem to problem 7.2 to your advantage!
  Problem 7.6(a): You can start from a result derived in problem 7.4 -- Solution 2
• HW 3 (due Thursday, Jan. 29, 2009) Jackson Problems 7.13 (part (a) only), 7.16, 7.22, 7.23
  Hints: For problem 7.22(b), Eq. (7.120) is not the most convenient starting point. Can you find a better one? -- Solution 3
• HW 4 (due Thursday, Feb. 12, 2009) Jackson Problems 6.5 (20 pts.), 7.30 (10 pts.), and extra problem (20 pts.) on integration using residues
  Hints: Problem 6.5a: For localized charge and current densities, how do the electrostatic potential and magnetic field fall off at large distance?
  Problem 6.5b: See p. 185 below Eq. (5.52) for technical help.
  Problem 6.5c: Puh, this was hard! Here is how I did it: Start from the surface term derived (and neglected) in part (a) and substitute the electrostatic potential in terms of E_0 as well as the magnetic field in terms of the current density, using Eq. (5.14) and a variation of the equation at the bottom of p. 29 in the text below Eq. (1.14). Now reverse the order of the volume and surface integrations. You do the surface integrals first -- these involve a symmetric tensor with an integrand proportional to n_a n_b /|x-x'|. This tensor can be expressed as Delta_ab = A n'_a n'_b + B \delta_ab where A and B are dimensionless functions of r'/r. (n and n' are unit vectors in x and x' directions.) Derive expressions for A and B by contracting the tensor indices appropriately and doing the surface integrals over a spherical surface using (3.38). When you have A and B, you have also Delta_ab and can then work out the remaining volume integral. (There are a few steps to be completed in between, such as working out the required derivatives of Delta_ab.) The last steps are identical to the last steps in part (b), except for a factor (-1/3). -- Yung-Yu points out that a (much) simpler solution uses Eq. (5.56).
  For Problem 7.30 you may find that an identity we derived last quarter (see lecture 6, p. 47) comes in handy!
  Extra problem: The point is not to get the correct result (Mathematica will give it to you), but to show how the integral is done using the residue theorem! -- Solution 4
• HW 5 (due Thursday, Feb. 19, 2009) Jackson Problems 9.2, 9.3 (hint: you will only need the electric dipole component), 9.7 (hint: repeat the steps done in class, Fourier-transforming all quantities into omega-space first, use \omega \exp(-i\omega t) = id_t \exp(-i\omega t), and then undo the Fourier transform), and 9.16 (omit radiation resistance in part (b)) (hint: use Eq. (9.8) in Jackson; see also Ch. 9.4 A) -- Solution 5
• HW 6 (due Thursday, Feb. 26) Jackson Problems 9.5, 9.11, 9.12, and 9.14 (20 pts.) [for part (a) you need the associated Legendre polynomials at zero argument -- see Abramowitz/Stegun 8.6.1] -- Solution 6
• HW 7 (due Tuesday, March 10, 2009, 11:59pm -- note nonstandard day!) Jackson Problems 10.1, 10.2, 10.3, 10.4 (a,b) (leave out the optical theorem part (c)), 10.7, and 10.11.
  This is the last HW set this quarter. It consists of 6 problems worth 60 pts. total, and you have 1.5 weeks for completing it. By popular demand, problems 10.7 and 10.11 in this HW are optional. So this HW set is worth 40 pts.(=100%), plus up to 20 bonus points.
  Hints: 10.1: You can sum over the two orthogonal linear polarizations or over left and right handed circular polarizations -- you'll get the same result.
  10.2 (a): You are asked to first generalize (10.71) (which does not assume long wavelengths) and then perform the long wavelength limit. After you are done, you are asked to compare with Problem 10.1 where the long wavelength limit is used from the beginning.
  10.3: (a) What do you know about the range of and the behaviour of the fields in the near zone in this situation? (b) Read the first Section of Chapter 8. The time-dependent fields can only penetrate a small distance \delta=skin depth into the conductor (given in Eq. (8.8)). This is where the oscillating incoming fields generate oscillating source currents (charge and current densities) that radiate, and this is also where the oscillating currents suffer resistance due to the finite conductivity which generates power losses. Use Eq. (8.12) to compute the power loss. To get the absorption cross section, you must normalize the lost power by the incident flux from the incident plane wave.
  10.4: (a) Use the results derived in class with a complex dielectric function appropriate for a conductor. (b) To get the absorption cross section, you must calculate the power dissipated in the sphere and normalize it by the incident flux (magnitude of Poyntimg vector). Where is power dissipated in this case? You can compute it by converting the surface integral of the Poynting flux into the sphere into a volume integral, using Poynting's and Ohm's theorems. -- Solution 7 (For a solution to problem 10.7 see Lecture 15.)

Exams:
Midterm Exam: Wednesday, Feb. 4, 2009, 8:00-10:18am in Smith 1180 (please note early start!)
Final Exam: Monday, March 16, 2009, 8:00-10:30am in PRB 1080 (please note non-standard room!)

Grading: 40% HW, 30% Midterm, 30% Final