Alternating current flows through a coaxial cable, the inner conductor of which is a solid and is of radius a. Because
of the skin effect, the current density distribution within the conductor is non-uniform and may be approximated by
\(J(r) = J_{0}e^{-(a-2r)}\)
where
\(J_{0}\)
is the current density at the surface of the conductor. The return current is through the outer conductor, which consists of an infinitely thin cylindrical shell of radius b. Use Ampere's law to calculate the magnetic field intensity everwhere.