Question

A coaxial cable has an inside conductor of radius 'a' carrying a current 'I'.The current returns as a uniform current through the outside conductor with a inside radius 'b' and outside radius 'c'.What is the magnetic field at a distance 'r' from the center, for the following cases.
r<a, a<r<b, b<r<c, c<r

Answer 1

You need to apply Ampere's law, which for a cylindrical geometry takes the form

B = uo I/(2 pi r)

Where uo is the permeability of free space and I is the total current inside radius r. Apply it in all regions. Assume the current is uniformly distributed in the inner and outer conductors.