A current loop, carrying a current of 5.0 A, is in the shape of a right triangle with sides 30, 40, and 50 cm. The loop is in a uniform magnetic field of magnitude 80 mT whose direction is parallel to the current in the 50 cm side of the loop. Find the torque on the loop.
This is the same current configuration as problem 54 in Ch. 29. You may solve for the torque by either of the methods advocated by the homework extension for that problem. For brevity, I present a quick calculation of the magnetic dipole moment of the loop, from which the torque is derived.
The dipole moment of a single current loop is proportional to the current and the area enclosed by the loop. The area for this triangle is 600 cm2, or 0.06 m2. Thus the dipole moment is (5.0 A)(0.06 m2) = 0.30 A-m2. The direction of the moment will be out of the screen (page) by the modified right-hand rule used for magnetic dipole moment assignment.
The torque on the loop is then proportional to the moment and the magnetic field strength. The moment is perpendicular to the field so the sine term is unity. The torque is thus (0.30 A-m2)(0.08 T) 0.024 N-m. The torque points upward.