A coaxial cable consists of a solid inner conductor with radius $$a$,$ surrounded snugly by

a material with outer radius $$b$.$ The inner conductor carries a free current I o along the

length of the conductor. A very thin conducting sheath located at s$=$b carries a free

current I o in a direction opposite of the inner conductor. The material between s$=$a and

s$=$b has a magnetic susceptibility $.$ Find the magnitude and direction of H$,$ B$,$ M$,$ Jb $,$ and

Kb everywhere.

Calculate the magnetic field a distance $10$ mm from a bare wire with radius $1$ mm

carrying a current of $10$ A$.$ Compare this to the magnetic field you might feel $10$ mm

from the outside of the coaxial cable described in this problem and explain why you

might want to use a coaxial cable instead of a bare wire. $($The Earth$$s magnetic field is

~$40$ T$).$