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Magnetic field, current with arced path

  1. Oct 21, 2013 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=63204&d=1382399172.png


    2. Relevant equations



    3. The attempt at a solution
    [tex]B=\frac{\mu_{0}I}{4\pi}\int \frac{dl\times \hat{r}}{r^{2}}=\frac{\mu_{0}I}{4\pi r^{2}}\int dl\times \hat{r}[/tex]
    So I think since when you cross dl with r, you end up with just dl.
    [tex]\frac{\mu_{0} I}{4\pi r^{2}}\int dl[/tex]
    l=rθ so dl=rdθ, substituting:
    [tex]\frac{\mu_{0} I}{4\pi r^{2}}\int rd\theta=\frac{\mu_{0} I}{4\pi r}\int d\theta=\frac{\mu_{0} I}{4\pi r}\theta[/tex]
    Plugging in values I end up with: 2.618x10-7 T

    Just need someone to look over work/logic, I think it's correct.
     

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  2. jcsd
  3. Oct 21, 2013 #2
    Just realized I could of just done the integral at ∫dl and plugged in rθ after, but whatever. Same result.
     
  4. Oct 22, 2013 #3

    rude man

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    Magnitude is correct.

    Direction?
     
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