Question

1. Magnetic Field Generated by a Current in a Wire Under steady-state conditions, a magnetic field B has curlB in a region where there is no current. We study the steady-state magnetic field B due to a constant current in an infinitely long straight thin wire. The magnitude of the magnetic field at a point depends only on the distance from the wire and its direction is tangent to the circle around the wire and determined by the right-hand rule. Suppose the current is flowing upward along the z-axis Then B is parallel to the ry-plane and, by the right-hand rule, points counterclockwise around a circle centered on the z-axis. (See Figure 20.26.) (a) Find the flux of curl B through the surface S between two concentric circles in the ry- plane of radius R1 and R2 centered on the wire (b) Calculate the circulation of B around each of the two boundary pieces of S, where their orientations are determined by the upward orientation of S (c) Use Stokes' Theorem to deduce that the magnitude of the magnetic field B is proportional to the reciprocal of the distance from the wire (d) Compare the magnitude B at two points P and Q if Q is twice as far from the wire as (e) To decrease the magnitude of B by 20%, by what factor does the distance from the wire have to increase? C2 Figure 20.26: Current along positive z-axis (out of page)

Answer 1

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