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NATF009, 7.5 hp

This is a PhD level course.

This course gives a basic introduction to electromagnetic field theory and some of its applications. The course is a reading or self-study course.

Course book

J. D. Jackson, Classical Electrodynamics, third edition, ISBN 0-471-30932-X.

What to read in the book

Part with exercises

  • Chapter 1: Section 1-11, 22 pages
  • Chapter 4: Section 1-3, 10 pages
  • Chapter 5: Section 1-8, 20 pages
  • Chapter 6: Section 1-4 and 6-7, 25 pages
  • Chapter 7: Section 1-5 and 7-9, 33 pages
  • Chapter 8: Section 1-4, 9 pages
  • Chapter 9: Section 1-3 and 4a, 12 pages

In total: 131 pages

Basic understanding only

  • Chapter I: Complete (prerequisite)
  • Chapter 12: Section 2, 2 pages
  • Chapter 13: Section 1-2, 7 pages
  • Chapter 14: Section 1-5, 16 pages
  • Chapter 15: Section 1-2, 13 pages

In total: 38 pages

Required Problems

  • 1.1
  • 1.5
  • 1.6
  • 1.14
  • 4.1
  • 4.4
  • 5.3
  • 5.7
  • 6.1
  • 6.5
  • 7.2
  • 7.3
  • 7.5
  • 7.13
  • 7.16
  • 8.1
  • 9.1
  • 9.8
  • 9.16

Problems to attempt (useful for understanding the later chapters)

  • 14.2
  • 15.2
  • 15.3

Hints and comments to some of the exercises

Don't forget 1.6d on the next page.
The first printing had a different (and wrong) version, use the latest one.
For part (a), it is much easier to prove for Cartesian multipoles and then use the relation between the two types of multipoles.
Part (c) can be solved via direct integration or by expanding in ρ and z and using the symmetries of the problem plus Maxwell's equations.
Part c can be easily solved by remembering that integrating over a sphere at a fixed radius r we have that int dS n_i n_j f(r) = 4π/3 δ_ij r^2 f(r)
It is enough to do it for one of the polarizations only, but note that once you have done one, the other is not much more work.
There are some overall phases missing in the answer given in part (a).
Add the interpretation of the averaging used in part (c), i.e. how you interpreted the expectation value mentioned. There seem to exist two versions of (b) in the different printings. The version you should solve is: repeat (a) but for an ideal conductor. Do you get the same answer?
The notation of the answer in (a) is confusing but correct. If you have problems, leave out the final integral over solid angle.
Beware you formula copiers, the current distribution is not of the form in the chapter, but similar enough so the solution should be doable. Final integral needed can be done numerically, it is feasible analytically but a little messy.

Some comments of the students and other possibly useful hints

  • I found the book by David J. Griffith, Introduction to Electrodynamics, useful as a help.
  • The open course ware at MIT, (search for physics and/or electromagnetism).
  • You can find many lectures on YouTube as well. I found several searching on for electromagnetism lectures.
  • You can also try the more general Open Courseware Consortium,
  • Some nice graphical illustrations of some of the principles can be found at Wolfram demonstrations,

Solutions on the web

There are many places with solutions to problems in Jackson available. The idea for you is to learn electrodynamics, not to figure out how to find someone else's solution. Try Google with jackson+electrodynamics+solutions and you will find many problems solved. But be careful, they are often wrong and/or have misunderstandings, so use them if you cannot find the solution yourself but make sure you understand what's going on.


Johan Bijnens, bijnens [at] thep [dot] lu [dot] se

Syllabus for course

Information about content, course goals and prerequisites.

Swedish original

English translation