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Ampere's Circuital Law

  1. Apr 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Using Ampere's circuital law, or otherwise, find the magnetic field B a distance r away from the axis of a thin walled circular hollow conductor of radius a and carrying a current I.

    2. Relevant equations
    [tex]\oint_L B\cdot dL = \mu_0I_{enclosed}[/tex]

    3. The attempt at a solution
    So far I have said:
    the conductor is a hoop. As a result inside the hoop (i.e. r<a) B=0 as [tex]I_{enc}[/tex]=0.

    However I am confused as to what line I should take to work out B when r>a. Does the system act like a long straight line (albeit in a circle) and the B-field is a loop around the hoop (cancelling out in the middle, and thus obtaining the same result for r<a), or is it some other shape all together?
  2. jcsd
  3. Apr 25, 2007 #2
    Outside the spherical shell, the magnetic field at a given point is constant. Therefore, [tex]B\oint dl=\mu_0 I_{enclosed}[/tex]. This would give you [tex]B=\frac{\mu_0 I_{enclosed}}{4\pi r^2}[/tex].
  4. Apr 25, 2007 #3
    Its not a spherical shell is it? I read it as just a circular loop.

    I think after a bit of playing with the numbers I get [tex]B = \frac{\mu_o I}{2\pi r}[/tex]
  5. Apr 25, 2007 #4
    How can a circular loop be hollow? As far as I can see, its a spherical shell. However, if it is a circular loop, you would be correct.
  6. Apr 25, 2007 #5
    It would just be a hoop as opposed to a flat disc.
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