# Note contribution to b 0 from the current in the

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Note: Contribution to B 0 from the current in the segment CA equals the contribution from the current in the segment AC 0 . Reason: This follows by noticing (from the Biot-Savart law) that the contribution to ~ B 0 from a current through the line element d ‘ centered about P is the same as the contribu- tion from an equal incremental line element d ‘ centered about P 0 with P and P 0 equally distant from point A . Thus each half of the extended wire gives the desired magnetic field B , and B + B = B 0 = μ 0 I 2 π a . Therefore B = μ 0 I 4 π a . Direct Way: Set up a coordinate system with the origin at A , such that the segment CA goes along the negative x -direction as in the figure. The distance from the field point O to the wire is a . Consider a certain point P along CA with x -coordinate x . The distance from O to this particular point is called r . Denote the (counterclockwise) angle between