On Oscillating Current Loop Radiation
Definition: An uncharged current loop is modeled as superimposed, equal density, counter-rotating rings of positive and negative charge.
Assumption: An uncharged current loop that translates in its plane is electrically polarized.
Fig. 1 depicts an uncharged current loop in the xy-plane. Its magnetic dipole moment points toward positive z. Its center is at rest. There is no electric polarization.
An Uncharged Current Loop
If the center of this current loop has the motion
then at time t=0 the bottom of the loop will be positively charged and the top will be negatively charged. The loop will have an electric dipole moment in addition to the omni-present magnetic dipole moment.
A quarter cycle later the center will be at rest at x=A. The electric polarization will have vanished. A half cycle later the center will be back at x=0, but now the bottom will be negatively charged and the top positively charged. Etc. As a result of relativistic effects, the oscillating loop constitutes an oscillating electric dipole. Presumably there will be electric dipole radiation.
There may also be radiation associated with the oscillating magnetic dipole. This would be similar to the radiation emitted by the oscillating permanent magnet depicted in Fig. 2 (which also has the motion specified by Eq. 1).
Oscillating Bar Magnet
Note that, to the extent the bar magnet can be modeled as an array of microscopic, uncharged current loops, both kinds of radiation will be manifest when the magnet is oscillated.
From the perspective of elementary particles, it is of theoretical interest that neutrons may emit electric dipole radiation when oscillating in the plane orthogonal to their magnetic dipole moments.
To the extent protons and electrons can be modeled as spinning rings of one-sign charge, there will not be translation-induced electric dipole moments when they oscillate in their planes. However, there will be imbalances of charge and this may have subtle effects on the fine details of emitted radiation when they are vibrated.
Of course in all such cases the energy of an electrically polarized loop is greater than that of the unpolarized state. Presumably a driving agent must expend extra energy to accommodate such a charge separation during one quarter of a cycle. But the system is "conservative" in that the expended work is recouped in the next quarter cycle when the loop reverts to an unpolarized state. Any energy attributable to electric dipole radiation is lost, however, and must be continually replenished by the driving agent.
It is noteworthy that the electric dipole radiation (or the electric polarization of a current loop) is not expected when the loop oscillates normal to its plane. To the extent nature prefers one phenomenon over another, this may suggest preferences for one orientation over another when neutrons (for example) are vibrated.