# EM Radiation of "Permanent" Molecular Electric Dipoles

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Suppose I were to subject a polar molecule to a high-frequency electric field. The polar molecule responds to the high-frequency electric field and thus it has a time-varying electric dipole moment vector. If we treated this as a classical electric dipole, it would be expected to radiate some of its internal energy in the form of electromagnetic waves. Of course, in quantum mechanics, this is not supposed to happen, otherwise such particles would constantly lose energy.

I can't help but wonder though, what if we had a ring of these "permanent" molecular electric dipoles that were oscillating, such that the produced electromagnetic field was essentially that of an alternating current in a closed loop? If we were to induce such an alternating "closed polarization" current loop, wouldn't the electric and magnetic fields of the permanent molecular dipoles collectively result in an outward-flowing Poynting vector, just as we might expect from the oscillation of induced dipoles?

Unlike the conduction current induced in a typical generator coil, the "closed polarization" current induced into a dielectric insulator would lead, not lag, with respect to the applied electric field (say, from an oscillating electromagnet). The electromagnetic field of the "closed polarization" current would induce a back-EMF into the electromagnet opposing changes in its current, and so the amplitude of the current through the electromagnet would reduce. Increasing the frequency of the applied electric field (i.e. increasing the frequency of the current through the electromagnet) would further increase this back-EMF, resisting even more the changes of current through the electromagnet, and thus limiting even more the amplitude of the current.

The magnetic field of the polarization currents would essentially be in phase (more or less) with respect to magnetic fields of the conduction currents in the electromagnet, as if to substitute for magnetization currents that would be produced by an iron core. Therefore, the back-EMF induced by such time-varying polarization currents would be out of phase with the currents in the electromagnet, and they would be off by 90 degrees if we neglect both propagation time delay as well as the dielectric relaxation time of the dielectric (i.e. the frequency, however high, is chosen to be low enough such that the oscillation period is much larger than the dielectric relaxation time of the insulator). The dielectric then behaves as if it possessed a frequency-dependent magnetic susceptibility which is only exists for AC magnetic fields while being non-existent for DC magnetic fields.

There would exist macroscopic electric fields produced by the changing currents in both the electromagnet and the dielectric material that impose the property of inductance. However, what about the "local electric fields" inside the dielectric that manifest as internal stresses? The local electric fields would act on electric dipoles in the insulator, and thus a kind of "self-interaction" occurs. Now normally you would think that such local electric fields would oppose the externally applied electric field. That is true if the source of the applied electric field is a potential gradient (thus irrotational), as we see with a "charged" capacitor, but not if the source of the applied electric field is due to a changing magnetic field (thus solenoidal). If the local electric fields produced internally were in phase, rather than in anti-phase, with the applied solenoidal electric fields, then it is clear that the strain on the dipoles would be significantly increased as both the local electric fields and the externally-applied solenoidal electric field act on them in the same direction.

For a dielectric material consisting of polar molecules to interact with its own local electric fields is essentially a self-interaction-type phenomenon, as it is an object distributed over space. The object can be large enough to where it is not assumed to reveal any quantum statistical phenomenon, and yet underlying it are fundamentally quantum entities (polar molecules each possessing a re-orientable "permanent" electric dipole, in addition to induced dipoles caused by both external and local fields). Suppose the dielectric was transparent to the induced EM wave frequency. So does the acceleration of the "permanent" components of the electric dipoles (i.e. that of polar molecules) permit the emission of electromagnetic waves beyond the physical volume of the dielectric, and if so does it draw upon (in part, but not solely) the kinetic energy of molecular rotations and vibrations in the process?

Sincerely,

Kevin M.

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