Stationary Equations
To derive the stationary equations, start with Ampère’s law for static cases:
∇ ×
H
=
J
. Define the potentials,
and the current
where
J
e
is an externally generated current density, and
v
is the velocity of the conductor.
Add the constitutive relationship,
B
= μ
0
(
H
+
M
)
, and rewrite Ampère’s law as
The equation of continuity is obtained by taking the divergence of Ampère’s law. It is the equation solved for the electric potential. Thus the following equations for
V
and
A
apply:
