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Calculating the magnetic field

  1. Oct 30, 2009 #1

    fluidistic

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    Gold Member

    1. The problem statement, all variables and given/known data
    A current whose density is [tex]\vec J[/tex] circulate through a conductor lattice infinitely long but with a depth [tex]a[/tex]. The current circulate in a direction which is parallel to the direction in which the lattice is infinitely long.
    1)Calculate the magnetic field [tex]\vec B[/tex] in a point [tex]P[/tex] situated at a distance [tex]d[/tex] from the center of the lattice.

    2. Relevant equations
    Ampère's law I guess.


    3. The attempt at a solution
    I had a hard time understanding the situation, but I finally think I got it.
    However here come my problems. [tex]\oint \vec B d \vec l = \mu _0 I = \mu _0 \int _S \vec J d \vec S[/tex], but I don't know what surface I should take as [tex]S[/tex].
    I've found [tex]\vec B = \mu _0 \vec J a[/tex]. Which is obviously wrong since I think I should get something like [tex]\frac{\text{constants}}{r}[/tex].
    Any help is greatly appreciated!
     
  2. jcsd
  3. Oct 30, 2009 #2
    imo, in this case, [tex]I = J.A = Ja^2 [/tex]

    From Ampere's law:

    [tex]
    \oint \vec B d \vec l = B . 2\pi d

    ==> B = Ja^2 / 2\pi d
    [/tex]

    p/s: im not sure that i understand your problem completely :(
     
  4. Oct 31, 2009 #3

    fluidistic

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    Gold Member

    Thanks for the help. I think the problem is like this : An infinite conductor plane with a depth of [tex]a[/tex]. The current flows in a direction. I have to calculate the magnetic field inside the lattice (from a depth of [tex]-\frac{a}{2}[/tex] if I consider the origin as being just over the lattice) and outside it.
    So I don't think that [tex]\oint d \vec l =2\pi d[/tex]. I'm unsure though.
     
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