Single-Particle Electrodynamics - Assassination Science

d −→ µ. (4.18)
We note carefully that we did not need to use Maxwell’s equations at all
in the analysis of the previous section; this is important because, under
a duality transformation, the homogeneous and inhomogeneous equations
are interchanged—and, indeed, need to be modified if magnetic charge and
current is introduced.
Under the transformations (4.18), we immediately find, for the nonrelativistic
analysis,
P = ( ˙µ·B) + (µ·∇)(v·B),
F = (µ·∇)(B − v×E) − ˙µ×E,
N = µ×(B − v×E). (4.19)
The rigorously relativistic analysis, in the rest frame of the magnetic-charge
dipole, likewise yields
P | v=0
= ( ˙µ·B),
F | v=0
= (µ·∇)B + (µ· ˙v)B − ˙µ×E,
N| v=0
= µ×B. (4.20)
The relativistically bootstrapped results for the magnetic-charge dipole are
therefore given by
ṗ = (µ·∂) ˜F ·U + [ ˜F · ˙µ ],
(Ṡ) = F ·µ + U(µ·F ·U). (4.21)
4.2.3 The electric-current magnetic dipole
We shall now analyse the most controversial form of magnetic dipole known
to physics: that due to the circulation of electric current. It is clearly the
only physically acceptable magnetic dipole model we have available to us;
129