A very long coaxial cable consists of an inner wire and a concentric outer cylindrical conducting shell of radius R. At one end, the wire is connected to the shell. At the other end, the wire and shell are connected to opposite terminals of the battery, so there is s current down the wire and back up the shell. Assume that the cable is straight. Find B (a) at points between the wire and the shell far from the ends (b) outside the cable.
Since there is the translational symmetry and the symmetry with respect to rotation about the axis of the cable, the magnetic field far from the ends of the cable can only have the azimuthal component ...
This solution describes how to determine the source of magnetic fields.