Description
Problems
1. Practice with Legendre polynomials: Consider a sphere of radius R (the center
is at the origin) where there are no charges inside and outside and any possible charge
is on the surface. The potential on the surface is φ|S = V (cos(θ)), θ is the inclination
angle, as usual counted from the z-axis.
(a) (20 pts) Using the method of separation of variables write down the general solution for the potential inside and outside the sphere as an expansion in Legendre
polynomials. Relate the coefficients of the expansion to φ|S.
(b) (15 pts) Find the solution for
φ|S = V0 cos(3θ).
(c) (15 pts) Find the electric field at the point (x = 0, y = 0, z = R/2) for the
potential in (b).
2. Summary of course topics (50 pts): Please compile your personal summary of the
course topics so far (special relativity and electrostatics up to and including cartesian
multipole expansion). This should not just be a list of all possibly useful equations you
can find. Your summary should reflect key concepts and the relations between them.
Make sure you understand the content of the equations you assemble and how to apply
them. (This assignment is intended to support your preparations for the exam. Please
try to present a clear view of the topics, but you may want to avoid spending too much
time just on perfecting the write-up.)
Physics 841 Homework 6
