Reading: Former reading assignment: Griffiths, Chapter 6, Sections 1-3 New improved reading assignment: Page 279-282, paying particular example to example 6.2. Read 284- 287, but skip example 6.3.

You may work together and get help from other students. Your solutions must be written in your own words, without looking at someone else’s solutions while you write them.

Don’t forget the 9 points that we are looking for in your solutions (see Moodle).

In order to make sure you get your context and meaning/make sense points, next to your answers, please put a “c” with a circle around it for context, and an “m” with a circle around it for meaning.

  1. Griffiths, Problem 6.16. (Coaxial cable with dielectric, good practice with Ampere’s law, and H)

  2. (this is really a chapter 5 problem) When particular materials are cooled below a certain critical temperature, they become superconductors. One property of a type I superconductor is that the magnetic field vanishes in its interior. Suppose a solid Type I superconducting sphere is placed in a constant, external magnetic field. Solve for the magnetic field everywhere outside the sphere. (Suggestion: in this case you can define a magnetic scalar potential, and use all the formalism we developed for solving Laplace’s equation using separation of variables.)

  3. A thin disk of iron of radius R and thickness \(t << R\) is magnetized in the direction parallel to the axis, \(M = M_0\hat{z}\) . Calculate H and B on the axis both inside and outside the iron. (I suggest you find the bound current using K = M cross r-hat and then call me over and let’s talk about it and your next steps.)

  4. A spherical permanent magnet has a uniform polarization M . Choose M to be along the z axis. Calculate B everywhere. Here’s a link with a “skeleton” solution to this problem. Please feel free to look at this as much as you want while working on the problem. https://www.overleaf.com/read/nbjymfcprkgx