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Magnetic Field of Two Wires

  1. Mar 9, 2008 #1
    [SOLVED] Magnetic Field of Two Wires

    1. The problem statement, all variables and given/known data

    [​IMG]

    If r = 30.0 mm, i = 2.00 A, and i' = 8.60 A, what is the magnitude of the magnetic field at the center point?

    2. Relevant equations

    B=([tex]\mu[/tex][tex]_{0}[/tex]I)/(2pi*r)

    3. The attempt at a solution

    I applied biot-savart's law to i and i', and added them together.

    For B_i:

    (4pi*10^-7*2)/(2pi*.03) = 1.34*10^-5

    For B_i':
    (4pi*10^-7*8.6)/(2pi*.03) = 5.74*10^-5

    B_center = B_i + B_i' = 7.08*10^-5

    Which is not correct. I'm pretty much sure my method at solving the problem is completely wrong. I just don't know what exactly is the right steps to take. Any help would be appreciated.
     
  2. jcsd
  3. Mar 10, 2008 #2

    jlg

    User Avatar

    biot-savart for a loop is u*2*pi*I/4*pi*R, which simplifies to u*I/2*R.. you're only looking for half a loop so 1/2 * that is equal to u*I/4*R ..

    The total mag field would thus be: u*I'/4*R + u*I/4*R

    u = 4*pi*10^-7, by the way.
     
    Last edited: Mar 10, 2008
  4. Mar 10, 2008 #3
    Ah, thanks! Got it.
     
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