Single-Particle Electrodynamics - Assassination Science

disks. The magnetic dipole moment then decays slowly to zero, due to this
frictional force. The crucial observation is that the time-changing magnetic
dipole force induces, by Maxwell’s equations, an electric field in the space
around the dipole. One can show that this electric field is given by
E(t) =
n× ˙µ
4πr 2 .
(This can, incidentally, also be obtained from the author’s retarded field
expressions of Chapter 5, even though the author only considers ˙µ’s for which
µ stays constant; it appears this result is quite general.) This electric field
acts on the charge, and gives it a mechanical momentum impulse. Because
the electric field depends on the rate of change of the magnetic moment, but
the impulse integrates this force up again, the net impulse is independent of
how slowly one lets the magnetic moment decay.
Shockley and James then point out that there is no apparent counterbalancing
force on the magnetic dipole! By taking the limit in which the
charge’s m/q ratio is made to approach infinity, the velocity attained by the
charge due to the imparted impulse can be made as arbitrarily small as one
likes, and hence there is no substantial magnetic field induced by the charge
that could act on the magnetic dipole. This may be taken to imply that the
mechanical momentum of the total system is not conserved.
Shockley and James suggested that a mechanical momentum excess contained
in the electromagnetic field is a “hidden momentum” of the magnetic
dipole; they then used this essentially as the ∆p of the Penfield–Haus effect.
However, this is manifestly incorrect, as the discussions of Chapter 2
show: the mechanical field momentum excess has already been counted in
the derivation of the Lorentz force law, which in turn yields the “textbook”
current loop force law. Thus, to add this excess field mechanical momentum
again would be to count it twice.
In fact, if one considers the question carefully, one finds that in fact there
are three aspects of the physical situation that all have a mechanical momen-
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