The figure below shows a cross section of a long coaxial cable. The inner wire of radius ? carriers total current ? that is flowing out of the page and is distributed uniformly over the cross-sectional area of the wire. The outer wire of inner radius ? and outer radius ? carries total current ? into the page. This current on the outer wire is distributed uniformly over the cross-sectional area of the outer wire and flows into the page.

a. Derive mathematical expressions for the volume currents flowing down the inner and outer wires.

b. Use the results of part ? and Ampere's law to calculate the magnetic field in the following four regions: (i) ?