A solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius b and outer radius c. The central conductor and tube carry equal currents in opposite directions. The currents are distributed uniformly over the cross sections of each conductor (Young and Freedman, 2013).
Derive an expression for the magnitude of the magnetic field:
(a) at points outside the central, solid conductor but inside the tube (a < r < c),
(b) at points within the outer conducting tube (b < r < c), and
(c) at points outside the tube (r > c).