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versions of the electromagnetic fields. The term Galilei invariant is used due to the fact
that they remain unchanged after a coordinate transformation of the type
r' = r + v0 t
In continuum mechanics, this transformation is commonly referred to as a Galilei
transformation.
The Galilei invariant fields of interest are
˜
E = E+vB
(Electromotive intensity)
˜
J = J – v
(Free conduction current density)
˜
-----PP =
+ v    P  –    v  P  (Polarization flux derivative)
t
˜
M = M + v  P (Lorentz magnetization)
˜
˜
B
H = ------ –  0 v  E – M (Magnetomotive intensity)
0
The electromotive intensity is the most important of these invariants. The Lorentz
magnetization is significant only in materials for which neither the magnetization M
nor the polarization P is negligible. Such materials are rare in practical applications.
The same holds for the magnetization term of the magnetomotive intensity. Notice
that the term 0v × E is very small compared to B/0 except for cases when v and E
are both very large. Thus in many practical cases this term can be neglected.
Air and Vacuum
The stress tensor in the surrounding air or vacuum on the outside of a moving object is
1
1
T
T
T
T 2 = – pI –  --- E  D + --- H  B I + ED + HB +  D  B v
2

2
There is an additional term in this expression compared to the stationary case.
Elastic Pure Conductor
The stress tensor in a moving elastic pure conductor is
1
1
T
T
T
T 1 =  M –  --- E  D + --- H  B I + ED + HB +  D  B v
2

2
where D0E and B0H.
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CHAPTER 2: REVIEW OF ELECTROMAGNETICS