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Magnetic field of bent wire for a point along parallel axis

  1. Nov 25, 2014 #1
    1. The problem statement, all variables and given/known data
    Long wire is bent such that it forms two parallel line segments that goes to -∞ along the z-axis and a semicircle of radius (R). Find magnetic field on Z axis.

    2. Relevant equations
    Biot-Savart Law
    (μ0/4π) I = ∫ dl' x R/ R^2

    where dl' is element of length and R is the unit vector, and R is the vector from source to point on z-axis

    3. The attempt at a solution
    So my attempt. I broke the problem into two parts. Magnetic field due to semicircle and magnetic field due to infinite wires.

    For the infinite wires I got

    B= μ0 I/2πR

    which I'm pretty sure is correct.

    The problem I'm having is calculating the magnetic field due to the semicircle

    dl' = Rdθ [sinθ, 0, cosθ]

    R = [Rcosθ, 0, Rsinθ+z]

    R^2= (Rcosθ)^2 + (Rsinθ+z)^2

    (dl' x R) = R^2+Rzsinθ dθ

    B = μ0/4π ∫ {(R^2+Rzsinθ)/(Rcosθ)^2 + (Rsinθ+z)^2 } dθ

    I feel like a made mistake somewhere.
    Since if z=0
    magnetic field due to the semicircle should be

    B = μ0*I/2R

    but thats not what my answer is showing.

    Any help would greatly appreciated.
    thanks
     
  2. jcsd
  3. Nov 28, 2014 #2

    Bystander

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    What's the orientation of the semicircle relative to the z-axis?
     
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