Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 314 / 3 / c / Solution

In an axisymmetric magnetostatic state, pressure and gravitational forces are poloidal, so the azimuthal component of the Lorentz force density must vanish. Hence $f=0$ andThe two gradients are locally parallel, so $L\alpha$ is constant on each regular level surface of $\beta$. Thereforefor an arbitrary flux function $F$.