1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper
    Gold Member

    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!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted