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Magnetic Field of A Toroid

  1. Dec 15, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm working through a proof that says the magnetic field of a toroid is circumferential at all points inside and outside the toroid. I can follow most of the proof, but am a bit confused where the first equation comes from.

    Here is the figure from the textbook (Griffith's 4th Ed).

    http://media.newschoolers.com/uploads/images/17/00/67/76/17/677617.jpeg [Broken]

    To begin the proof, Griffiths starts with the field at [itex]\mathbf{r}[/itex] due to the current element at [itex]\mathbf{r}'[/itex].[tex]d\mathbf{B}=\frac{\mu_0}{4\pi}\frac{\mathbf{I}\times\mathbf{\hat{{u}}}}{u^3}dl'[/tex]

    2. Relevant equations

    [tex]\mathbf{B}=\frac{\mu_0}{4 \pi}\int\frac{\mathbf{I}\times\mathbf{\hat{u}}}{u^2}dl'[/tex]

    3. The attempt at a solution

    I'm just confused at how Griffiths got from the Biot-Savart law above, into the equation he posted in the question. (I replaced the script r with a u). Where does the cubed term come from?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Dec 15, 2013 #2
    I believe that is a mistake in the text. I think he meant it to be the vector r and not r hat, in which case the denominator would be cubed.
     
  4. Dec 16, 2013 #3

    rude man

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    I agree with post #2. Otherwise the dimensions don't check out.
     
  5. Dec 16, 2013 #4
    cool thanks. I was thinking that, but I wanted to confirm!
     
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