find all the bound currents. What is the net bound current flowing down the wire?

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1. The problem statement, all variables and given/known data

A current I flows down a long straight wire of radius a. The wire is made of linear material with susceptibility chi(subscript m), and the current is distributed uniformly.

i) what is the magnetic field a distance s from the axis?
ii) Find all the bound currents. What is the net bound current flowing down the wire?

3. The attempt at a solution
i) I found a similar homework question on this website:

http://maxwell.uncc.edu/gjgbur/cours...k11answers.pdf

which says that B=[mu Is/(2pi a^2)]phi-hat
ii) J(subscript M)= curl M
= [(chi(subscript M) I)/(pi a^2)] z-hat

integral of [(chi(subscript M) I)/(pi a^2)] z-hat dS
= loop integral of [(chi(subscript M) I)/(pi a^2)] z-hat. dl
=0

why does J(subscript M) have to be integrated over the surface, though?

j(subscript m)=M cross n-hat
=[- chi(subscript M) Is/(2 pi a^2)]z-hat ?

why does http://maxwell.uncc.edu/gjgbur/cours...k11answers.pdf
say that j(subscripr m) has to be integrated over the perimeter? How do I do this? And why is the result of it supposed to be zero? Please help