USAPhO 2010 Semi-Final Problem A2

A spherical shell of inner radius a and outer radius b is made of a material of resistivity \rho and negligible dielectric activity. A single point charge q_{0} is located at the center of the shell. At time t=0 all of the material of the shell is electrically neutral, including both the inner and outer surfaces. What is the total charge on the outer surface of the shell as a function of time for t>0 ? Ignore any effects due to magnetism or radiation; do not assume that b-a is small.