Magnetostatics Equation
To derive the magnetostatic equation, start with Ampère’s law for static cases
∇ ×
H
=
J
. The current is
where
J
e
is an externally generated current density, and
v
is the velocity of the conductor.
Using the definitions of magnetic potential,
B
= ∇ ×
A
and the constitutive relationship,
B
= μ
0
(
H
+
M
), rewrite Ampère’s law as
which is the equation used in magnetostatics.
The term involving the velocity only applies in the 2D and 2D axisymmetric formulations.
