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Magnetic field

  1. Aug 10, 2009 #1
    1. The problem statement, all variables and given/known data

    the current density is given by J(p) = (I/pi) * p^2 * e^(-p^2) in z direction
    The question is to first show that the cureent flowing through the wire is 'I' and then to find then to find the B field.

    2. Relevant equations

    stokes theorem.
    integral of B.dl = I

    I = J.dS

    3. The attempt at a solution

    i can find the magnetic field. however i am stuck on the first part that requires me to proof the total current is I.
    I set up the problem in cylindrical coordinates and tired the double integration between 0 to 2pi and o to a(arbitsry distance) however this does not give the correct result. plese point me in the right direction
     
    Last edited: Aug 10, 2009
  2. jcsd
  3. Aug 10, 2009 #2

    alphysicist

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    Hi iontail,

    Can you verify your equation? You have:

    J(p) = (I/pi) * p^2 * e^(-x^2)

    Is that supposed to be p^2 in the exponential instead of x^2? Also, can you show your work for the integration?
     
  4. Aug 10, 2009 #3
    sorry about that it is supposed to b p^2, a typo. I tried integrating by parts on the ,p, terms and using the cylindrical coordinates formula for for dS. I get e^-p(p+3) as result
     
  5. Aug 10, 2009 #4
    i updated the question as well
     
  6. Aug 10, 2009 #5

    alphysicist

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    I don't believe the integral should be cut off at an arbitrary limit (like you are doing with the quantity a); instead the radial varible p should be integrated from 0 to infinity. If you are still getting the wrong answer, please post the integration steps you are taking.
     
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