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Stokes therem and Current

  1. Aug 22, 2009 #1
    i am trying to solve this problem which states that

    J(p) = (I/pi) p^2 e^-p^2 in z direction
    is the current density flowing in the vicinity of insulating wire.
    pi = pie

    in standard spherical polar coordinates.

    J is the current density.

    I need to prove that the total current flowing through the wire is I.

    I have tried to used the idea J.dS = I where

    and integrate(i have taken the scale factor into consideration) but it does not yield the right result. Any suggestion on a way to move forward will be appreciated.
     
  2. jcsd
  3. Aug 22, 2009 #2

    Born2bwire

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    What are the limits of integration here? Still, I can't see how you can get a current of I because of your exponential, except if your relationship is incorrect.

    [tex]J(\rho)=\frac{I}{\pi}e^{-\rho^2}[/tex]

    If we have a wire of infinite size then this one would work, but this is just playing around.
     
  4. Aug 22, 2009 #3

    jtbell

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    You missed a factor of [itex]\rho^2[/itex]:

    [tex]J(\rho)=\frac{I}{\pi} \rho^2 e^{-\rho^2}[/tex]
     
  5. Aug 23, 2009 #4

    Born2bwire

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    That's his original equation yes, whose integral over the cross-sectional area of the wire I think will be

    [tex]I(\rho)=-I_0e^{-\rho^2}(\rho^2+1)+I_0[/tex]

    Seeing as the OP has not given us the dimensions of the wire we can't go any further than that but I do not see how any normal choice of radius would allow the current to come out to be exactly I_0. I was just mentioning that if the \rho^2 dependence was dropped then, the integral would come out provided an infinite radius but as I stated I was not seriously suggesting that was an answer.

    Another question is what does Stokes' Theorem have to do with the problem. I feel that there were some steps leading up to this point that the OP may have left out.
     
    Last edited: Aug 23, 2009
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