Single-Particle Electrodynamics - Assassination Science

The fact that the Penfield–Haus effect returns us to practically the same
equation of motion as the magnetic-charge dipole means that the undesirable
properties of the current-loop equations of motion are no longer applicable;
we instead return to the manifestly satisfactory properties of the electric
dipole case.
(The extra contact force can be easily shown to not lead to
any change in the mass of the particle either.) Thus, since the mass m is a
constant, we can write down the covariant equation of motion, in terms of
the four-velocity U, immediately:
m ˙U = (µ· ∂) ˜F · U + [ ˜F · ˙µ] + µ×J ×U; (4.57)
the final term is the covariant generalisation of the contact force µ×J, and
the partial derivative [ ˙µ] encompasses the new redshift force, as with the
electric dipole. The covariant spin equation of motion is of course just the
Bargmann–Michel–Telegdi equation:
(Ṡ) = F ·µ + (µ·F · U)U. (4.58)
Equations (4.57) and (4.58) are essentially the final classical equations of
motion the author shall present for a fixed pointlike magnetic dipole (ignoring
radiation reaction, which will be considered in Chapter 6).
4.2.5 Literature on the current loop force law
If the reader finds the Penfield–Haus effect interesting, they will find some
of the literature on the subject simply fascinating. At essentially the same
time as Penfield and Haus were doing their work on the subject, Shockley
and James [188] constructed a beautiful gedanken experiment that showed
that something was definitely amiss with the standard textbook force on a
current loop. They essentially placed a stationary charged particle at some
distance from two counter-rotating charged disks (their electric-current magnetic
dipole), and then introduced a very small frictional force between the
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