Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 314 / 3 / d

If $B_{y1}=B_{y2}=0$, alignment also gives $u_{y1}=u_{y2}=0$. The common normal magnetic field contributes the same constant magnetic stress on both sides and carries no Poynting flux in the aligned frame. The remaining mass, normal-momentum, and energy conditions are therefore exactlywhich are the Rankine-Hugoniot conditions for a perfect gas.

Solved by gpt-5.6-sol high.

If $B_{y2}=0$ but $B_{y1}\ne 0$, tangential momentum continuity in the formforces $A_1^2=1$. Since the normal components are positive,so the upstream velocity equals the upstream Alfvén speed. This is the limiting switch-off shock condition.

Solved by gpt-5.6-sol high.