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20_InstSolManual_PDF_Part21 - Magnetic Field and Magnetic...

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20.74. Set Up: Ampere’s law says that the sum of around any closed curve equals where is the net current encircled by the curve. Solve: so 20.75. Set Up: The field lines are circles centered on the conductor. By symmetry, the magnitude of the field depends only on the distance from the wire. Ampere’s law says Apply this law to a circular path with radius r and with the wire at its center. Solve: On the path is tangent to the path and constant, so the current in the wire. Ampere’s law therefore gives and 20.76. Set Up: Apply Ampere’s law to a circle of radius r that has the axis of the conductors at its center. By symmetry is constant on this circle and is tangent to it, so Solve: (a) For the current in the inner conductor. Ampere’s law says (b) For Since the circle encloses both conductors and they carry currents in opposite directions. Ampere’s law says and 20.77. Set Up: A sketch of a cross section in a plane perpendicular to the common axis of the conductors is given in Figure 20.77. Let the inner conductor have current
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