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Point where magnetic field cancels between two current carrying wires.

  1. May 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Problem statement along with relevant diagram attached with picture below.


    2. Relevant equations
    The Biot-Savart Law for a long current carrying wire.
    B = (μ)(I)/2(pi)(d)
    Where d is the perpendicular distance between the wire and the point at which the field is being calculated. μ is the permeability of free space.

    3. The attempt at a solution
    (a) Point at which field is null:
    Net magnetic field = 0.
    Thus, the sum of the magnetic fields at a certain point is 0. (One will point into the page and one will point out of the page)
    Thus:
    Bnet = 0 ⇔ (μ)(I1)/2(pi)(ρ) = (μ)(I1/2)/2(pi)(d - ρ)
    Calculate ρ. I think it works out to be 2d/3.
    Could someone tell me if this is correct?
    Also, for part (b) what adjustment should be made? Assuming I did (a) correctly. Thanks.
     
  2. jcsd
  3. May 17, 2013 #2
  4. May 17, 2013 #3

    haruspex

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    Sounds right.
    What change do you think it makes to the field from I2?
     
  5. May 18, 2013 #4
    Will both fields be pointing out of the page (in the positive k) in the region of 0-d?
     
  6. May 18, 2013 #5
    Sorry! I meant into the page. In the negative k.
     
  7. May 18, 2013 #6

    haruspex

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    Yes, but I meant, what difference does it make to the equation?
     
  8. May 18, 2013 #7
    Well. instead of having:
    (I)(μ)/(2)(pi)(ρ) - (I/2)(μ)/(2)(pi)(d - ρ) = 0

    We'll now have:
    (I)(μ)/(2)(pi)(ρ) + (I/2)(μ)/(2)(pi)(d - ρ) = 0
    I think the answer works out to be ρ = 2d.
     
  9. May 19, 2013 #8

    haruspex

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    Looks right.
     
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