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Homework Help: Magnetic field of two current-carrying wires crossing over

  1. Jun 3, 2012 #1
    Two long current-carrying wires cross at an angle of 21° ("theta" is half of this) as shown in the figure above. The magnitude of the current is the same in each wire, I=400 A.

    A wood mouse is running along the dashed line midway between the wires towards the point where the wires cross. The mouse turns back at point P, some distance x from the wire crossing point, because the magnetic field strength reaches an unbearable 6.8 mT. Determine the distance x (in cm).

    Okay, so I assigned the dotted line perpendicular to one of the wires (in the triangle of interest in the diagram) as 'r' and...

    I did:

    B=(μ0/2pi) x I/r
    so r =μ0/2pi x I/B
    r=(2x10^(-7) x 400)/6.8
    Therefore r = 1.176x10^(-5)

    Now using sine
    sin(theta) = r/x
    therefore x = (1.176x10^(-5))/(sin(10.5))
    =6.45 x 10^(-5)
    or 6.45x10^(-3)cm

    The weird thing is if i multiply that by two and move the decimal i have 12.9cm which is close to the correct answer of 12.91cm. Maybe I have stuffed up the formula or the units somewhere....

    Also i'm aware the question is in millitesla so maybe i should have used 0.0068T in my first equation. However when I compute this I still get the wrong answer.

    If you can help that would be great, I thought I was doing this the right way but maybe there is another way.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

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  3. Jun 3, 2012 #2
    Hi ness87. The distance from both wires at P are equal and the fields due to both are the sum of their individual fields. So the field would be [itex]B=2\frac{\mu_0I}{2{\pi}r}[/itex]. Using [itex]B=6.8\times10^{-3}[/itex] T also, gives you a factor of 2000 off from the answer
  4. Jun 3, 2012 #3
    Ahhh! Fantastic, yes that makes sense to do twice the field strength because both fields contribute. Great!

    Thank you very much sleepy time, much appreciated
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