Physics 318 R.G. Palmer Electromagnetism 4/7/10

Physics 318
R.G. Palmer
Assignment 7 (due Monday 4/12/10)
1. Jackson’s problem 3.1
2. Jackson’s problem 3.4
3. Jackson’s problem 3.5
4. Jackson’s problem 3.10
5. Consider a region constructed from the intersection of two concentric spheres, radius a and b (with
b > a) and a right-angle cone. Specifically, in (r, θ, φ) coordinates, a ≤ r ≤ b, 0 ≤ θ ≤ π/4, and
0 ≤ φ ≤ 2π. Suppose that there is a fixed potential V0 on the r = b surface, and zero potential on the
other two surfaces. Find an expansion for the potential everywhere in the region, and make a contour
plot of the equipotentials for the case b = 2a.
Note: In Mathematica (or something like it) you’ll have to set up functions to find the appropriate roots
of Pν (cos θ0 ) = 0, and to do two types of integrals. The result should converge pretty well except near
some of the boundaries.