Suppose there is a configuration with coaxial current carrying cylindrical (infinitely long) conducting tubes as shown with one having radius a and the other having radius b. The currents on each of the tubes is I in the directions shown. There is an insulating material of permeability µ between the tubes. a) What is the magnetic field B between the tubes? b) What is the bound bulk current J, between the tubes (away from the boundaries at s = a and s = b)?

An infinitely long wire is wrapped around an infinitely long cylinder of radius R making n turns per unit with steady current I. If the cylinder axis points into/out of the page, determine the directions of the velocity for a charged particle that is launched inside the cylinder such that it experiences zero magnetic force.

Please answer parts (a), (b), and (c).

Two parallel, infinitely straight lines currents, I1 and I2, (but opposite in direction) are separated by a distance d. Find the magnitude of the force per length between them (“force per length” so that it wouldn’t be an infinite force between them). Indicate whether the force would be attractive or repulsive.