Experiments show that a steady current in a long wire produces a magnetic field that is

Chapter 13, Problem 13.2.40

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Experiments show that a steady current in a long wire produces a magnetic field that is tangent to any circle that lies in the plane perpendicular to the wire and whose center is the axis of the wire (as in the figure). Ampres Law relates the electric current to its magnetic effects and states that where is the net current that passes through any surface bounded by a closed curve and is a constant called the permeability of free space. By taking to be a circle with radius , show that the magnitude of the magnetic field at a distance from the center of the wire is

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