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The classical electromagnetic self-force on an arbitrary time-dependentelectric or magnetic dipole moving with constant velocity in vacuum, and in amedium, is considered. Of course, in vacuum there is no net force on such aparticle. Rather, because of loss of mass by the particle due to radiation, theself-force precisely cancels this inertial effect, and thus the spectraldistribution of the energy radiated by dipole radiation is deduced without anyconsideration of radiation fields or of radiation reaction, in both thenonrelativistic and relativistic regimes. If the particle is moving in ahomogeneous medium faster than the speed of light in the medium,Vavilov-\v{C}erenkov radiation results. This is derived for the differentpolarization states, in agreement with the earlier results of Frank. Thefriction experienced by a point (time-independent) dipole moving parallel to animperfectly conducting surface is examined. Finally, the quantum/thermalEinstein-Hopf effect is rederived. We obtain a closed form for the spectraldistribution of the force, and demonstrate that, even if the atom and theblackbody background have independent temperatures, the force is indeed a dragin the case that the imaginary part of the polarizability is proportional to apower of the frequency.

physical review research

Self-force on moving electric and magnetic dipoles: dipole radiation,  Vavilov-\v{C}erenkov radiation, friction with a conducting surface, and the  Einstein-Hopf effect