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Parallel wires carrying current out of the page, find B

  1. Mar 13, 2015 #1
    1. The problem statement, all variables and given/known data
    Two parallel wires are a distance 2 b apart from the origin and carry current I out of the plane of the paper.
    Find the magnitude and direction of the magnetic field B(y) along the y axis.

    2. Relevant equations
    ∫B⋅dl=μI




    3. The attempt at a solution
    If we take ∫dl = 2πr
    B=μI/(2πr)
    r=√(b^2+y^2)

    Clearly the y components cancel so we are left with only the horizontal components, that is

    B_total=2Bcos(θ)

    cos(θ)=b/√(b^2+y^2)

    However, in the answer key provided, it says that cos(θ)=y/(b^2+y^2)

    I don't understand why this would give this horizontal component. It seems like this would give the vertical component.
     
  2. jcsd
  3. Mar 13, 2015 #2
    Nevermind, I see how. The angle made by the B field from each wire and the horizontal is not the same as the angle between r and b
     
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