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    The Magnitude and Direction of Magnetic Fields

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    Point P is midway between two long, straight, parallel wires that run north-south in a horizontal plane. The distance between the wires is 1cm. Each wire carries a current of 1A toward the north.

    A) Find the magnitude and direction of the magnetic field at point P.
    B) Repeat the question if the current in the wire on the east side runs toward the south instead.

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    Solution Preview

    Please see the attachments for the solution.

    First, let's calculate the field of an infinite wire carrying a current I.

    From symmetry we can conclude that the magnitude of the magnetic field is constant on a concentric circular path of radius r around the wire. The direction of B is always perpendicular to the current and the radius (Biot-Savart law) -hence it is tangential to the loop.
    If we use Ampere's law that states ...

    Solution Summary

    This response determines the magnitude and direction of a magnetic field at a specific point.