$82.$ A coaxial cable has an inner conductor of radius a $,$ and outer thin cylindrical shell of radius b$.$ A current Iflows in the inner conductor and returns in the outer conductor. The selfinductance 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$).$

I saw a similar question on chegg but it was asked to calculate the self$-$inductance per length. In that question they calculated the magnetic flux per unit length by integrating B$($r$)$ with respect to dr$.$ What I want to know is if I need just the slef inductance of the whole thing. Do I integrate B$($r$)$ wrt dA$.$ Where dA$=2*$pi$*$l$*$dr for part a if l is the length of our cylinders and dA$=(2*$pi$*$l $+4*$pi$*$r$)*$dr$.$ If possible please solve the question step by step.