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Magnetic flux thorugh a loop of wire

  1. Dec 23, 2006 #1
    1. The problem statement, all variables and given/known data
    Griffiths Problem 7.8
    A square loop of wire (side a) lies on a table dsiantce s from a very long straight wire, which carries a current I, as shown in teh figure.

    Find the flux of B through the loop

    2. Relevant equations
    Flux of B is given by
    [tex] \Phi_{B} = \int \vec{B} \dot d\vec{a} [/tex]

    3. The attempt at a solution
    THe area element is constant
    but hte magnetic field is not
    For a wire, B at a dsitance r is given by
    [tex] \vec{B} = \frac{\mu_{0} I}{2\pi r} \hat{phi} [/tex]

    Flux is then
    [tex] \Phi_{B} = \int_{s}^{s+a} \frac{\mu_{0} I}{2\pi r} a^2 ds [/tex]

    but hte solution says that the area element should be just a, and not a^2 .. why is that???

    thanks for help!

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  3. Dec 23, 2006 #2

    Doc Al

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    Staff: Mentor

    The element of area is "a ds", where "ds" is distance along r: you are treating the area as infinitesimal rectangular strips, parallel to the wire.
  4. Dec 23, 2006 #3
    thank you
    i get it now
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