We consider three different definitions of magnetic dipole moment for electrically neutral compact bunches of charged particles and show that, in general, they are not equivalent to each other with respect to their relativistic transformation. In particular, we prove that the "configurational" definition of magnetic dipole moment mc = 1/2∫v(r × j)dV (in the common designations) and its definition through generated electromagnetic field ("source" definition ms) or experienced force ("force" definition mf) lead to different relativistic transformations of mc and ms (mf). The results obtained shed light on the available disagreements with respect to relativistic transformation of a magnetic dipole moment, and they can be used in covariant formulation of classical electrodynamics in material media.
Alexander L. Kholmetskii,
Oleg V. Missevitch,
"Relativistic Transformation of Magnetic Dipole Moment," Progress In Electromagnetics Research B,
Vol. 47, 263-278, 2013. doi:10.2528/PIERB12110903
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