Single-Particle Electrodynamics - Assassination Science

introduced to them before, not because they exhibit any inherent complexity.
In fact, if one examines the terms in (5.75) and (5.76) particularly, one finds
that, really, they are pretty well what one would expect to find, simply on
dimensional and consistency grounds. For starters, one knows that, since the
fields are being generated by a electric dipole moment d—represented here
by d σ,—each term in the field expressions must contain one, and only one,
factor of σ ′ , or one of its time-derivatives. Furthermore, one knows that,
simply on dimensional grounds, the terms in the 1/R 2 and 1/R fields must
contain a total of one and two overdots, respectively—since the three-vectors
v, σ ′ , n, and their cohorts, are all dimensionless. One is then simply left
with the therapeutic pastime of slotting together the available three-vectors,
and the available number of overdots, into terms of the correct parity (axial
vectors for the terms in braces in (5.75); polar vectors for the terms in (5.76)).
As already noted, the three-vector v is itself only used once; a priori, one
would not expect such a dramatic simplification of the gameplay. From here,
one must then simply sprinkle the scalar factors γ and κ (and the numerical
coëfficient 3) around liberally, for one to end up with expressions looking like
(5.75) and (5.76).
In any case, regardless of their æsthetic merit, the author believes the expressions
(5.75), (5.76), (5.77), (5.78), (5.79) and (5.80) to be most definitely
correct, so one will now have to live with them, regardless of one’s opinions
of them.
5.5 The static fields
We now wind back the throttles on our analytical engines somewhat, to provide
an overview of the standard textbook problem of obtaining the static
fields of a point particle carrying electric charge and electric and magnetic
dipole moments; and, in particular, the behaviour of these fields at the position
of the particle.
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