Electromagnetic Field Theory I

Physics 834, Autumn 2009

Welcome to the Physics 834 home page! The course information is available here plus lots of supplementary info. Please check this page regularly.

Recent additions to this page:

*** There will be an extra class on Friday, Nov. 20, 8:30-10:30am, in the Smith Seminar Room (PRB 1080) ***

CONTENTS:

• Instructor and TA contact information
• Topics
• Textbook and additional reading references
• Lecture Notes
• Homework assignments and solutions
• Exam schedule and grading

Instructor and TA contact information:

Office: M2046 Physics Research Building (PRB) (phone: 688-5363)

Office Hours: Mondays 11:00 am - 12:00 pm; Tuesdays 10:30 am - 11:30 am

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

Grader: Zhi Qiu (office: PRB M2043; office hours: Thursdays 3:30-5:30pm; phone: 247-2367; email: qiu@mps.ohio-state.edu)

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Topics:

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Textbook and additional reading references:

• 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 does not cover everything we will discuss in class)

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Lecture Notes:

• Chapter 1: Introduction to Electrostatics
  • Lecture 1 (9/23/09)
• Lecture 2 (9/28/09)
• Lecture 3 (9/30/09)
• Lecture 4 (10/5/09and 10/7/09)
• Chapter 2: Boundary Value Problems in Electrostatics I
  • Lecture 5 (10/7/09 and 10/12/09)
• Lecture 6 and Dr. Horowitz's lecture notes (10/14/09)
• Lecture 7 (10/19/09)
• Chapter 3: Boundary Value Problems in Electrostatics II
  • Lecture 8 (10/21/09)
• Lecture 9 (10/26/09)
• Lecture 10 (10/28/09)
• Midterm review pages (10/31/08)
• Lecture 11 (11/02/09)
• Lecture 12 (11/04/09)
• Chapter 4: Multipoles, Electrostatics of Macroscopic Media, Dielectrics
  • Lecture 13 (11/16/09)
• Lecture 14 (11/18/09)
• Lecture 15 (11/20/09)
• Chapter 5: Magnetostatics, Faraday's Law, Quasi-Static Fields
  • Lecture 16 (11/23/09)
• Lecture 17 (11/25/09)

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Homework assignments and solutions:

Homeworks are due at 11:59 pm on the due date. Please put them in the grader's mailbox in PRB or give them to me in class (or slide them under my office door if the other options are not available). Homeworks submitted late are penalized -10 pts. The cutoff for late HW submissions is 5 pm on the day after the HW is due.
(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, Sep. 30, 2009) Jackson Problems 1.3, 1.4, 1.5, and one more problem
  Hint for Problem 4: For the second form of the delta-function, you can do the normalization integral (ii) by complex contour integration (residue theorem). (Don't just look it up in MATHEMATICA!) For this you should first integrate by parts (why?) -- Solution 1
• HW 2 (due Wednesday, Oct. 7, 2009) Jackson Problems 1.7, 1.9, 1.11, and 1.12 -- Solution 2
• HW 3 (due Wednesday, Oct. 14) Jackson Problems 2.4, 2.7, 2.9, and 2.11 (20 pts.)
  Here is a hint for Problem 2.11. -- Solution 3
• HW 4 (due Wednesday, Oct. 21) Jackson Problems 2.13, 2.15, 2.23(a), and 2.24 -- Solution 4
• HW 5 (due Wednesday, Oct. 28) Jackson Problems 3.9, 3.10, 3.17, and 3.23.
  Hint: Various types of completeness relations, such as (3.139), (3.108) with x and k interchanged, (2.46), etc. may come in handy!
  Another hint for 3.10(b): check out section 2.10 of Jackson's text!
  The solution to 3.10 builds on the result from 3.9; the solution to 3.23 partially builds on 3.17.
  3.9: What consideration dictates whether you want to expand the rho-dependence in Bessel or modified Bessel functions? Which sign of the separation constant should you use for the z-dependence?
  3.10(b): In the limit of large L the leading term should exactly reproduce the result for problem 2.13 from last week's homework.
  3.17: This is an application of the same methods we developed in class. Fill in all missing steps, so that you become proficient in these methods. The final results are given -- the path to get there is the problem. The final expressions tell you which sets of orthogonal functions to expand in, which basically tells you which way to proceed. (You need completeness relations in terms of the sets of functions used in the expansion!)
  3.23: Use the representations for the Green functions derived in problem 3.17 and in class. How do you get from the Green functions to the potential Phi? -- Solution 5
• HW 6 (due Thursday, Nov. 5) Jackson Problems 3.1, 3.2, 3.3, and 3.4.
  Hint for Problem 3.1: If in doubt about which "known results" to check your solution against, look at Eq. (3.36) in the text book.
  Problem 3.2: Which equation do you need to solve here, Laplace or Poisson? What do you remember about solving the Poisson equation? Do you know the Green function appropriate for this problem? In part (c), when taking the limit of a large hole, the leading term is zero, so you must go to next-to-leading order in the expansion around \alpha=\pi.
  Problem 3.3: The potential on the z-axis can be computed analytically. Match it to an expansion in Legendre polynomials to compute it off-axis. Make sure your result takes the proper limits at r \to \infty and r \to 0.
  Problem 3.4: You may find it useful to compute or look up the Fourier series for a square wave. Use parity arguments to eliminate terms in the series without having to compute them explicitly. For a given number n of bisecting planes, make a list of the first few l and m values of the non-vanishing coefficients in the spherical harmonic expansion. For part (b), evaluate those that have l less or equal to 3. To answer the last question, draw a sketch of the situation you computed and the situation treated in Eq. (3.36). How do you get from one to the other? Relate the polar and azimuthal angles in each case to each other by expressing (x,y,z) in terms of (x',y',z') using the respective decomposition in spherical coordinates. So, for example, if the y axis in one problem corresponds to the z' axis in the other problem, this implies that \sin\theta \sin\phi = \cos\theta' (why?). At the end, you should find perfect agreement of your result, evaluated up to order l=3, with Eq. (3.36). -- Solution 6
• HW 7 (due Thursday, Nov. 19) Jackson 3.5, 3.6, 3.14 (20 pts.), 4.1, 4.2, 4.7(a,b) (20 pts.) [total point value of this set is 80 pts.]
  Hint for problem 3.5: The expression (a) is almost identical with (2.19) in the text - read the text leading to that equation!
  Hint for 3.6: This problem looks familiar, doesn't it?
  Hint for problem 3.14: you can start from the master formula (1.44) and use the Dirichlet Green function for concentric spheres (3.125). What is the charge density you should use in (1.44)?
  Hint for 4.7: Write the given charge density as a superposition of spherical harmonics and use their orthonomality for the calculation of all its multipole moments. Part (b) amounts to a comparison of the exact potential (which you are asked to calculate) with the first few terms of its multipole expansion. Separate terms that fall off exponentially from power-law terms. -- Solution 7
• HW 8 (due Wednesday, Nov. 25, 5:00pm sharp (no exceptions) -- PLEASE NOTE NON-STANDARD DUE DATE!) Jackson 4.9 and 4.10 (20 pts. each, 40 pts. total)
  -- Solution 8

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Exam schedule:

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