Magnetostatics Equation

To derive the magnetostatic equation, start with Ampère’s law for static cases ∇ × H = J. The current is

where Je 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 = μ0 ( H + M ), rewrite Ampère’s law as

which is the equation used in magnetostatics.