Single-Particle Electrodynamics - Assassination Science

its discovery. Mathematically, the above prescription of course arises because
the quantity
(r· ˙v)
has the same position dependence as the quantity
(r·∇)
in the Taylor expansion of the fields. However, the author does not yet have
any intuitively simple explanation of why the prescription (4.45) is physically
correct. We leave this as an exercise for the reader.
We now turn to the redshift correction to the force expression. As with
the above, the detailed analysis again finds that this extra contribution may
be obtained by means of the redshift prescription (4.45):
F redshift = ˙v(µ·B).
4.2.4 Mechanical momentum of the current loop
We now ask the following loaded question: What is the mechanical momentum
of a stationary electric-current magnetic dipole?
Before we answer this question, let us first explain its importance. In
Chapter 2, we continually (and somewhat pedantically) reminded the reader
that the force on a particle is the time rate of change of its mechanical momentum:
F ≡ d t p.
This is the only definition of “force” permissible. If you were to inscribe the
laws of physics on stone tablets, this would go on the first one.
Now, a point mass, possessing no other characteristics at all, has the
following kinematical relationship between its velocity and its mechanical
momentum:
p ≡ mγv. (4.46)
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