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In a magnetostatic equilibrium, inertia is absent and all forces balance. A force-free magnetic field is the limiting case in which the Lorentz force density vanishes:Thus the current density is parallel to the magnetic field, so for some scalar force-free parameter $\alpha (\mathbf{r})$,Using Ampère's law in magnetostatics givesTaking the divergence and using both the divergence of a curl is zero and $\nabla \cdot \mathbf{B}=0$ yieldssoThe force-free parameter is therefore constant along every magnetic field line.

A force-free magnetic field obeysequivalently $\mathbf{j}\times \mathbf{B}=0$: its current is parallel to its magnetic field. In a very low-density exterior, material pressure and inertia are too small to balance a finite Lorentz force. Quasistatic force balance therefore drives the magnetic field toward a force-free configuration.

The magnetic energy isUsing the ideal-MHD induction equation and integrating the identity $\mathbf{B}\cdot \nabla \times (\mathbf{u}\times \mathbf{B})$ by parts givesThe volume term vanishes for a force-free magnetic field, leaving