Single-Particle Electrodynamics - Assassination Science

hazard a guess that, if one were to shake the magnet around vigorously, some
sort of electromagnetic radiation should, by rights, be “shook off”—just as
happens with an electric charge. However, an analogue of the radio antenna
example is, in this case, not so easy to think of. And what about exact
expressions for the electomagnetic fields generated by magnets, in arbitrary
motion: are these in all the standard textbooks? The student would be sadly
disappointed if they assumed so.
There is, fundamentally, no good reason why the fields generated by magnetic
or electric dipoles, in arbitrary motion, should be treated any differently
to those generated by electric charges—other than that of pure lack of interest.
Particles carrying dipole moments do, naturally, require a somewhat
more careful treatment than those simply carrying electric charge—after all,
they contain a certain amount of “structure”; but, on the other hand, the
particles of Nature, to which we usually apply the equations of classical
electrodynamics, generally come with magnetic dipole moments already installed:
a fundamental particle without a magnetic moment is a rarity.
To repair this deficiency in most textbooks’ treatments of the retarded
electromagnetic fields, we will, in this chapter, derive explicit expressions for
the fields generated by a point particle carrying electric and magnetic dipole
moments, as well as electric charge—and, moreover, will obtain them in a
very simple form. The mood of the author, in this chapter, is to essentially
provide a derivation of the retarded dipole fields that could, with very little
work, be grafted on as an extra section in Jackson’s textbook [113]—the
concepts, methods and notation used essentially mirroring those used in that
text.
In Section 5.2, we briefly review the history of the search for the retarded
fields for particles with dipole moments. In Section 5.3, we review the derivation
of the standard Liénard–Wiechert fields for an electrically charged point
particle, both to ground our notation, and to establish the general method
of attack on such problems. We then, in Section 5.4, turn these techniques
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