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Ampere's Law: Toroid

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data

    A toroid of a circular cross section whose center is at the origin and the axis the same as the z-axis has 1000 turns with po=10cm, a=1cm. If the toroid carries a 100mA current, find |H| at (6cm, 9cm, 0).



    2. Relevant equations

    How do I calculate |H| at certain points?



    3. The attempt at a solution

    Knowing that H = NI / 2*pi*po, and po - a < p < po + a, I have found p to be between 9cm and 11 cm.

    I assumed H = H1 + H2.

    If H1 = ((1000)(0.1) / 2 * pi * 0.9) * (0.06x + 0.09y) = 10.61x + 15.92y
    Similarly, H2 is the same except p = 0.11 m. Therefore H2=8.68x + 13.02y.

    After adding the two, and then finding the magnitude I get 34.8 A/m, but the answer is 147.1 A/m.
     
  2. jcsd
  3. Sep 28, 2009 #2

    kuruman

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    I don't know what H1 and H2 are and you don't explain. Look, you have a formula that gives H as a function of the radius. Everywhere at that radius the field is the same. So, at what radius is point (6 cm, 9 cm, 0)?
     
  4. Sep 28, 2009 #3
    H1 and H2 are H, except one is calculated at 9cm and one is calculated at 11cm. H, I'm assuming, is the sum.
     
  5. Sep 28, 2009 #4

    kuruman

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    No it is not the sum. At a given radius r

    [tex]H=\mu_{0}\frac{N I}{2\pi r}[/tex]

    The above expression says "You give me the radius, I will give you H."

    So, at what radius is point (6 cm, 9 cm, 0)?
     
    Last edited: Sep 28, 2009
  6. Sep 28, 2009 #5
    Ok thank you! That helps a lot. Even if I do find 'r', what do I do with the a and p values?
     
  7. Sep 28, 2009 #6

    kuruman

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    What do the a and p values represent?
     
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