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Homework Help: Auxiliary Field H Problem, Asks for Magnetic Field etc

  1. Mar 31, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    int[H*dl] = I fenc

    ∇×H = cr^2 [Khat]

    ∇×H = Jf

    3. The attempt at a solution

    The textbook I have been assigned (griffiths) only deals with currents that are uniformly distributed and I'm not sure how to go about calculating the free enclosed current for the problem. If I knew how to do that, this problem would be very easy.

    Using an amperian loop that extends the radius of the cylinder

    ∫(closed)H*dl = I fenc

    |H|[2*pi*s] = I fenc
    H = I fenc / [2*pi*s] [phi hat direction]

    Then I would use the cross product ∇×H = Jf in order to calculate Jf, sub in Jf = cr^2 and then solve for c, thus solving part a. I'm just not sure about how to calculate the free enclosed current. if anyone knows the proper formula for this problem I would be grateful to see it.

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    Last edited by a moderator: Mar 31, 2013
  2. jcsd
  3. Mar 31, 2013 #2


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    Hi laz0r. Welcome to PF!

    Regarding finding the proportionality constant c: If you integrate Jfree over the cross-sectional area (a<r<b) what should that equal?
  4. Apr 1, 2013 #3
    Ah ok, I understand now. INT[J*dA] = Ifree, then you can use that for your H field later on and find the expression for c immediately by rearranging.
  5. Apr 1, 2013 #4


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    You should be able to get c from just ∫J[itex]\cdot[/itex]dA = Io
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