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Magnetism - the proportionality constant question

  1. Jan 5, 2006 #1

    Hi! Can anyone please tell me where this equation was derived from?
    This equation is used to get the magnetic field (B).
    I is current and r is the distance. And I think I understand the Meu. And yet I have no idea where the 2pi came from. I looked in my textbook, internet and asked friends but nobody seems to know.

    Thank you!
    Last edited: Jan 5, 2006
  2. jcsd
  3. Jan 5, 2006 #2


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    That is the magnitude of the magnetic field carried by a long wire. I think you meant r instead of y in the equation you displayed. You obtain it by simple application of Ampere's Law and the [itex]2\pi r[/itex] comes from integrating around a circle of radius r (i.e. it's the circumference of the circle).
  4. Jan 5, 2006 #3
    Well, that's the magnetic field from an infinite straight wire, which you can get using Biot-Savart:

    [tex]d\vec{B} = \frac{\mu_0}{4\pi} \frac{I \vec{dl} \times \hat{r}}{r^2}[/tex]

    Biot-Savart is derived from Ampere's Law:

    [tex]\int_C \vec{B} \cdot \vec{dl} = \mu_0 \int_S \vec{J} \cdot \vec{da}[/tex]
  5. Jan 5, 2006 #4
    aha, thank you!
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