1 W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism, 2nd ed. (Dover, New York, 2005), Section 18-6.
2 We use Gaussian units since the relativistic aspects of relations among the dipole moments are displayed most clearly in these units.
3 Reference 1, Section 18-4.
4 D. Bedford and P. Krumm, “On the origin of magnetic dynamics,” Am. J. Phys. 54, 1036-1039 (1986).
5 D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Prentice Hall, Upper Saddle River, 1999), Problem 12.62.
6 This situation is somewhat paradoxical since we shall see that, unlike the acquired electric dipole moment, the acquired magnetic dipole moment is not a relativistic effect.
7 A. O. Barut, Electrodynamics and Classical Theory of Fields and Particles (Dover, New York, 1980), Chapter II, Section 4.
8 G. E. Vekstein, “On the electromagnetic force on a moving dipole,” Eur. J. Phys. 18, 113-117 (1997). [OpenAIRE]
9 G. P. Fisher, “The electric dipole moment of a moving magnetic dipole,” Am. J. Phys. 39, 1528-1533 (1971).
10 J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), Problems 6.21, 6.22 and 11.27 (a).
11 When a time dependence of the electric dipole itself is allowed, the polarization current density (7) is supplemented by a term p˙ 0δ(r − r0(t)), where the dot denotes the time derivative. It can be shown easily that this term generates already in the dipole's rest frame a magnetic field (p˙ 0 × n)/c|r − r0(t)|2, where n is the unit vector (17); this magnetic field must be then added to the moving dipole's magnetic field (14).
12 The magnetic force on a moving electric dipole p0, which is the Lorentz force on the sum (11) of the polarization and magnetization currents, can be derived in the Lagrangian formalism using an interaction −m · B, where m = −v × p0/c. See V. Hnizdo, “Comment on 'Electromagnetic force on a moving dipole',” Eur. J. Phys. 33, L3-L6 (2012); arXiv:1108.4332.
13 Reference 10, Problem 6.22.
14 See, e.g., Reference 10, Sec. 5.6.
15 It can be shown easily by integration by parts that (1/2c) R d3r r × Jm, where Jm = c∇ × [m δ(r−r0)], equals the magnetic moment m in the curl expression for Jm.