Question

A direct current I flows in a long round uniform cylindrical wire made of paramagnetic with susceptibility x. Find: 

(a) the surface molecular current I'_s;

(b) the volume molecular current I_v';

How are these currents directed toward each other?

Answer 1

Inside the cylindrical wire there is an external current of density  This gives a magnetic field Hφ with

The surface current is obtained by using the equivalence of the surface current density to  this gives rise to a surface current density in the z-direction of 

The total molecular surface current is,

The two currents have opposite signs.