Overview
Magnostatics deals with situations where there exists a steady current somewhere in space.
{% \frac{\partial \rho}{\partial t} + \nabla \cdot J = 0 %}
When the current is static, we assume that
{% \rho = 0 %}
that is, the electrons that move through one region are immediately replaced by the electrons moving into that region.
(the charge density is zero, even though there are charges moving around).
THis implies that
{% \nabla \cdot J = 0 %}
Amperes Law
{% \nabla \times \vec{B} = \mu_0 \vec{J} %}