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

  1. 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/coursepages/4231assets/homework11answers.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/coursepages/4231assets/homework11answers.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
     
  2. jcsd
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