Single-Particle Electrodynamics - Assassination Science

We assume that the electric and magnetic dipole moments of the body
are, in fact, parallel, in the following discussion; this has not been assumed in
the previous sections of this chapter, but is, of course, the case for spin-half
particles.
5.5.7 Mechanical field expressions
The densities of the electromagnetic mechanical energy, mechanical momentum
and mechanical angular momentum are given by [113, Sect. 6.8]
W ρ (r) = 1 2{
E 2 (r) + B 2 (r) } , (5.94)
p ρ (r) = E(r)×B(r), (5.95)
s ρ (r) = r×p ρ (r). (5.96)
It should be noted that, due to the nonlinearity of these relations, we must
consider all of the possible combinations of multiple moments explicitly: we
cannot superpose the results for the moments considered individually.
5.5.8 Electric charge mechanical field properties
If the body possesses electric charge only, then, since it generates no static
magnetic field, relations (5.95) and (5.96) show that its mechanical selfmomentum
and mechanical angular self-momentum vanish identically. From
(5.81) and (5.94), its mechanical self-energy is given by
m q e.m. = 1 ∫
d 3 r q2 r 2
2 rε 16π 2 r 4
= 3q2
20πε
≡ 1 2 q2 η 1 , (5.97)
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