Problem
Consider a uniformly charged cylindrical shell with radius R and length L. The shell is spinning with angular velocity ω about the z-axis of the cylinder. (i) Let the cylinder be open-ended, i.e. there is no top or bottom to the shell. The total charge of the shell is Q. Find the magnetic field at the center of the shell. (ii) Now imagine there is a top and a bottom to the shell that also spin with angular velocity ω. The top and bottom are also uniformly charged, let's say they each have total charge q, while the charge from part (i) remains Q. Find the total magnetic field at the center of the shell