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Homework Help: Compute flux through rectangular area

  1. Mar 15, 2010 #1
    1. The problem statement, all variables and given/known data

    There is an aXb rectangular area in the same plane as a wire with current I. The wire is parallel to side b, and a distance d away. Compute the flux through the rectangular area.

    2. Relevant equations

    [tex]\Phi[/tex]=[tex]\int[/tex]B*dA

    B=([tex]\mu[/tex]I)/(2[tex]\pi[/tex]r)

    cylindrical coordinates... rdrd[tex]\theta[/tex]dz
    3. The attempt at a solution
    ([tex]\mu[/tex]I)/(2[tex]\pi)[/tex][tex]\int[/tex][tex]\int[/tex][tex]\int[/tex](1/r)(rdrd[tex]\theta[/tex]dz)

    dr is from d to d+a
    d[tex]\theta[/tex] is from 0 to 2[tex]\pi[/tex]
    dz is from 0 to b

    The solution to this ends up having natural logs in it, and to do that I would have to drop r, but I don't feel like that is right. Could someone please help point me in the right direction on setting up this integral.

    Thank you.
     
  2. jcsd
  3. Mar 15, 2010 #2
    Re: flux

    I am not sure why some things look like subscripts or exponents so just a warning there are no exponents are subscripts lol
     
  4. Mar 16, 2010 #3
    Re: flux

    I think I see why now. I should be using rectangular coordinates huh?
    I don't know what I was thinking... I must have been thinking partially of amperes law
     
  5. Mar 16, 2010 #4
    Re: flux

    ([tex]\mu[/tex]I)/(2[tex]\pi)[/tex][tex]\int[/tex][tex]\int[/tex](1/r) dr dy

    dr from d to d+a
    dy from 0 to b

    would this be the correct set up?
     
  6. Mar 16, 2010 #5

    ideasrule

    User Avatar
    Homework Helper

    Re: flux

    Yes, that's the correct setup. Your solution should have a natural log in it.
     
  7. Mar 16, 2010 #6
    Re: flux

    [tex]\frac{ \mu I }{2\pi} \int_0^b \int_d^{d+a} \frac{1}{r} dr dy [/tex]

    Code (Text):

    \frac{ \mu I }{2\pi} \int_0^b \int_d^{d+a} \frac{1}{r} dr dy
     
    Hope that helps, though it's nothing to do with the actual question.
     
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