A direct current `I` flows in a long round unifrom cylindrical wire made of permagnetic with sesceptibility `chi`. Find
(a) the surface molecule current `I_(s)`,
(b) the volume mulecule current `I'_(v)`.
How are these currents directed toward each other?

Explanation

Inside the ball cylindrical wire there is an external current of density `(l)/(pi R^(2))`. This gives a magnetic field `H_(varphi)` with
`H_(varphi) 2pi r = l (r^(2))/(R^(2))` or, `H_(varphi) = (Ir)/(2pi R^(2))`
From this `B_(varphi) = (mu mu_(0) Ir)/(2pi R^(2))` and `J_(varphi) = (mu - 1)/(2pi) (Ir)/(R^(2)) = (chi Ir)/(2 R^(2))` = Magetization.
Hence total volume molecular current is,
`oint_(r = R) vec(J_(varphi)).d. vec(r) = int (chi I)/(2pi R) dl = chi I`.
The surface current is obtained by using the equivalence of the surface current density to `vec(J) xx vec(n)`, this gives rise to a surface current density in the z-direction of `- (chi I)/(2pi R)`
The total molecular surface current is,
`I'_(s) = (chi I)/(2pi R) (2pi R) = -chi L`.
The two currents have opposite signs.