Halliday, Resnick & Walker — Magnetic Fields: Problem 9

9 Prove that the relation \(\tau = NiAB \sin \theta\) holds not only for the rectangular loop of Fig. 28-19 but also for a closed loop of any shape. (Hint: Replace the loop of arbitrary shape with an assembly of adjacent long, thin, approximately rectangular loops that are nearly equivalent to the loop of arbitrary shape as far as the distribution of current is concerned.)