Torque on a Current Loop

Section §3.10.5 found the force on a single straight current-carrying wire in a field. A loop of current-carrying wire has forces acting on all of its sides at once; in a uniform field these forces cancel to give zero net force, but they generally do not cancel as a torque -- this leftover torque, which tends to spin the loop, is exactly the principle behind every electric motor, and (run in reverse, measuring the torque …