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Magnetic field between two long, straight wires

  1. Oct 31, 2009 #1
    1. The problem statement, all variables and given/known data

    Capture3.JPG

    2. Relevant equations

    [tex]B = \frac{\mu_o i}{2\pi d}[/tex]

    3. The attempt at a solution

    To do this, you'd find the magnetic field magnitude due to the left wire, and add it to the magnetic field due to the right wire. Correct?

    If so:

    Wire 1:
    [tex]B = \frac{1.26x10^-6 (8)}{2\pi(.02)} = -4x10^-6 \hat k[/tex]

    Wire 2:
    [tex]B = \frac{1.26x10^-6 (12)}{2\pi(.02)} = 1.2x10^-5 \hat k[/tex]

    But this isn't right. The answer is B.

    What's gone wrong?
     
  2. jcsd
  3. Oct 31, 2009 #2
    You just forget to add 2 B together.
    [tex]
    B1 = \frac{\mu_o i1}{2\pi d} = \frac{20 \mu_0}{\pi}
    [/tex]

    [tex]
    B2 = \frac{\mu_o i2}{2\pi d} = \frac{30 \mu_0}{\pi}
    [/tex]

    Total B at midpoint is:

    B = B1 + B2

    Because direction of B1 is in opposite that of B2 and B2 > B1, so you should choose direction of B2 as positive direction.

    ==> B = B2 - B1
     
  4. Oct 31, 2009 #3
    Hmm. I thought that's what I was doing. I must have put something into the calculator incorrectly because I got something else for B1. But when I just did it, following what you did, it works out.

    Thanks.
     
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