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Magnitude of the magnetic field produced by a wire

  1. Mar 2, 2009 #1
    1. The problem statement, all variables and given/known data
    A power line carries a current of 95 A along the tops of 8.5 m high poles. What is the magnitude of the magnetic field produced by this wire at the ground?


    How does this compare with the Earth's field of about 1/2 G?


    2. Relevant equations

    B= uo[tex]\mu[/tex]/2[tex]\pi[/tex]I/r

    3. The attempt at a solution
    4[tex]\pi[/tex]e-7/2[tex]\pi[/tex]95/8.5
     
  2. jcsd
  3. Mar 2, 2009 #2

    Delphi51

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    Homework Helper

    The formula is not appearing quite right on my screen, but you clearly have the right one. Is there any difficulty remaining?
     
  4. Mar 4, 2009 #3
    Use Ampere's Law:
    [tex]\oint B \bullet dl = \mu_{0}I[/tex]

    integrate around a closed circle of radius 8.5m centered around the wire. Since each infinitesimal point dl around the circle's circumfrence will have the same magnetic field passing through it (and because teh B field is perpendicular to the circle at all points) the entire wire has the same magnitude of magnetic field passing through it.

    So the integral reduces to:

    [tex]B\oint dl = \mu_{0}I[/tex]
    [tex]B * 2 * \pi * r= \mu_{0}I[/tex]
    [tex]B = \frac{\mu_{0}I}{2 * \pi * r}[/tex]

    where r is the radius of the circle 8.5M and I is the current in the wire 95A.
     
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