Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 314 / 1 / c / Solution

Define the accumulated rotation angleThe coupled first-order equations describe a rotation of $(B_y,B_z)$ and have the general solutionDirect differentiation verifies both force-free equations, and $B_y^2+B_z^2=C_1^2+C_2^2$ is constant. Thus a one-dimensional force-free magnetic field rotates without changing its magnitude.