A <force-free magnetic field> obeys
$$
(\nabla\times\mathbf B)\times\mathbf B=0,
$$
equivalently $\mathbf j\times\mathbf B=0$: 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.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-314/4/a/solution