A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b

A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b. A current I flows in the inner conductor and returns in the outer conductor. The self-inductance of the structure will depend on how the current in the inner cylinder tends to be distributed. Investigate the following two extreme cases.
(a) Let current in the inner conductor be distributed only on the surface and find the self-inductance.
(b) Let current in the inner cylinder be distributed uniformly over its cross-section and find the self-inductance. Compare with your results in (a).