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Quick Magnetic Field Question

  1. Nov 25, 2007 #1
    1. The problem statement, all variables and given/known data

    One wire, lying on the x-axis, carries a current of 8.0 A in the positive x-direction. Another wire, lying on the y-axis, carries a current of 12 A in the positive y-direction. What is the magnitude of the magnetic field at (x, y) = (8.0 cm, 12.0 cm)?

    2. Relevant equations

    B = (uI) / (2*PI*r)

    u = 4*PI*10^-7

    3. The attempt at a solution

    First, I found each magnetic field seperately.

    B1 = ((4*PI*10^-7)(12)) / (2*PI*(8/100)) = 3*10^-5 T
    B2 = ((4*PI*10^-7)(8)) / (2*PI*(12/100)) = 1.3*10^-5 T

    This is the point I am stuck. The answer key says the answer is 1.7*10^-5 T. I see that you can get that answer by:

    3*10^-5 T - 1.3*10^-5 T = 1.7*10^-5 T

    However, I do not understand the reasoning behind this. Could somebody explain this to me? Thanks in advance.

    Travis Walters
  2. jcsd
  3. Nov 25, 2007 #2

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    For the Ix, the field at the given pt is toward +ve z, and for Iy, the field is toward -ve z.

    Think about how the magnetic field lines are circular about the wire. Here, at the given point, they are in opp directions.
  4. Nov 25, 2007 #3
    Hey there,

    I see what you mean about them being in opposite directions.

    However, since B1 is in the negative Z direction, would that answer be -3*10^-5 T instead of 3*10^-5 T? Likewise, since B2 is in the positive Z direction, would that answer be 1.3*10^-5 T instead of -1.3*10^-5 T?

    If that is the case adding these two quantities togather would yield -1.7*10^-5 T and not 1.7*10^-5 T correct? Is the magnitude the absolute value or should it be negative?

    Thanks once again for any clarification.

    Travis Walters
  5. Nov 25, 2007 #4

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    The magnitude is simply the absolute value without regard to the sign and so is always +ve.
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