Torque on slowly moving electric or magnetic dipoles in vacuo

Abstract

The torque on a moving electric or magnetic dipole in slow motion is deduced using the Lorentz transformation of the fields to first order in v/c. It is shown that the obtained equations are independent of the model adopted for the dipole, whether it is of Amperian or Gilbertian type, thus showing the complete validity of the Amp\`ere equivalence principle even in dynamical conditions. The torque is made of three terms: beside that due to the direct torque on the dipole there are two more terms: one due to the torque on the associated perpendicular dual-dipole caused by motion, while the other is the inertial torque due to the displacement of the dipole which carries with it the field linear momentum, or the hidden momentum.