Electrodynamics of moving dipoles: The case of the missing torque Available to Purchase

In a recent article, Bedford and Krumm [‘‘On the Origin of Magnetic Dynamics,’’ Am. J. Phys. 54, 1036 (1986)], examine in detail the interaction between a moving line of charges and a magnetic dipole consisting of a conducting ring of current from the point of view of different frames of reference. One particular orientation of the magnetic dipole leads to an apparently paradoxical situation of a torque acting in one inertial frame but not in another. These authors explain the situation by considering the rate of change of mass of the charge carriers and a wall force that prevents them from accelerating in the direction of their motion. They also hint at an intriguing analogy with some kind of inertial or fictitious force such as occurs in noninertial frames. First, the general expression is derived for the torque on a moving magnetic dipole in any orientation and the term representing the missing torque is explicitly revealed. Then the physical origin of this torque is investigated in the particular case considered by Bedford and Krumm, where the magnetic dipole consists of a small current‐carrying conducting loop. It appears that, in this case, the elusive torque arises from the interaction between the current carriers in the magnetic dipole loop and the magnetic field due to the surface current generated by the motion of the induced charges on the surface of the conducting loop.