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Determining magnitude of net force with three parallel wires

  1. Jul 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Three parallel wires carry a current of I 1 = 3 A, I 2 = 2 A, and I 3 = 1 A, respectively. They are arranged as shown. If r = 2m and L=5m,what is the magnitude of the net force on the bottom wire?
    <------------------------- I1
    r
    -------------------------->I2

    2r

    <--------------------------I3

    I1 = 3A I2 = 2A I3 = 1A r = 2m L = 5m
    They show the radius from I1-->I2 as r and the radius from I1-->I3 as 3r


    (a) 0 N
    (b) 5×10−7 N
    (c) 2×10−7 N
    (d) 3×10−7 N


    2. Relevant equations
    F = ILBcosθ
    B = μo * I/ 2∏r


    3. The attempt at a solution

    I feel like I am missing a concept here.

    B = (1.257e-6)(1A)/2(Pi)(2) = 1.00028e-7
    F = ILB = (1)(5)(1.00028e-7) = 5.0014e-7

    The answer is supposed to be 0N. I was thinking the first two wires might cancel out, but I am really not too sure. I don't see any other concepts. I also tried the right hand rule to determine the direction of Force. I feel pretty lost at this point.
     

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    Last edited: Jul 5, 2012
  2. jcsd
  3. Jul 5, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    This, with the right hand rule, is what you need.

    Hints:
    When figuring out the B field at I3 due to I1, what distance will you use? What value of I?

    When figuring out the B field at I3 due to I2, what distance will you use? What value of I?
     
  4. Jul 5, 2012 #3
    The distance used with I3 would be 3r and I2 would be 2r? The Current for I3 being 3A and for I2 being 2A, right?
     
  5. Jul 5, 2012 #4

    Doc Al

    User Avatar

    Staff: Mentor

    I'll reword that. We want to calculate the B field created by I1 at the position of wire 3. So we need the distance between wire 1 and wire 3, which is 3r.

    And we also want to calculate the B field created by I2 at the position of wire 3. So we need the distance between wire 2 and wire 3, which is 2r.
    When finding the B field due to wire 1, we use the current I1 (which is 3 A). When finding the B field due to wire 2, we use the current I2 (which is 2 A).

    So find the magnitude and direction of those two B field contributions. Then you can add them up to find the net B field at wire 3 due to the other two currents.
     
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