Fields and Moments of a Moving Electric Dipole

where the inertial lab frame moves with velocity v with respect to the (inertial) rest frame of the polarization densities, and γ = 1/ √ 1− v2/c2. Considerations of the fields moving electric dipoles perhaps first arose in the context of Čerenkov radiation when the dipole velocity v exceeds the speed of light c/n in a medium of index of refraction n [3]. Later discussions by Frank of his pioneering work are given in [4, 5]. As noted by Frank [5], specialization of eq. (1) to point electric and magnetic dipole moments p and m, and to low velocities, leads to the forms p ≈ p0 + v c × m0, m ≈ m0 − v c × p0, p0 ≈ p− v c × m, m0 ≈ m+ v c × p, (2)