186 Sources of the Magnetic FieldQ30.4No total force, but a torque. Let wire one carry current in the ydirection, toward the top of the page. Let wire two be a millimeterabove the plane of the paper and carry current to the right, in the xdirection. On the left-hand side of wire one, wire one creates magneticfield in the zdirection, which exerts force in the ±± ±ik j×=−direction onwire two. On the right-hand side, wire one produces magnetic field inthe −±kdirection and makes a ±±±ikj×− =+ejforce of equal magnitude acton wire two. If wire two is free to move, its center section will twistcounterclockwise and then be attracted to wire one.12FIG. Q30.4Q30.5Ampère’s law is valid for all closed paths surrounding a conductor, but not always convenient.There are many paths along which the integral is cumbersome to calculate, although not impossible.Consider a circular path around but notcoaxial with a long, straight current-carrying wire.
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