Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 314 / 4 / a / Solution

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.