Consider an infinitely long coaxial cable in which two equal currents/run in the opposite direction as indicated in Fig. I below

(a) Assuming that the magnetic permeability of all the materials is approximate that of vacuum, determine the magnetic field strength everywhere inside and outside the cable under the assumption that the current density is uniform within the conductors. (Do not forget to properly define your positions in a 3D coordinate system or with respect to the center line of the cable.) Graphically indicate the direction of the magnetic field lines in the cross-sectional sketch in Fig. 1.

(b) Assuming that the insulating plastic and copper are linear materials with re- respective magnetic susceptibility Xm. = 1.3 x 10-6 and me = -9.7 x 10-6, determine the magnetic field strength everywhere. Comment on where the magnetic field varies continuously and where it is discontinuous. 

(c) Explain in words what the sign of the magnetic susceptibility Xm means in terms of the microscopic process that is going on when these two materials are exposed to an experimental magnetic field. How would you experimentally detect material with a negative Xm (such as water)? 

Crossection Side view