Magnetostatics MOC
Magnetostatics is a special case of electrodynamics where the Magnetic field is time-independent and there is no electric field, i.e.
Magnetostatics was established empicircally by the Biot-Savart Law, but of course it is fully encoded in Maxwell’s equations whose differential form become
whence it immediately follows that
Since the Poynting vector and thus momentum density vanishes, no energy nor momentum is transported by the fields and no momentum is stored by the fields.
Potential
A magnetostatic system is completely described by its magnetic potential
where the Coulomb gauge
so for localized sources the solution is
for volume, surface, and line current density respectively. See also Multipole expansion of the magnetostatic potential.