If $B_{y2}=0$ but $B_{y1}\ne0$, tangential momentum continuity in the form
$$
B_{y2}(A_2^2-1)=B_{y1}(A_1^2-1)
$$
forces $A_1^2=1$. Since the normal components are positive,
$$
\boxed{A_1=1},
$$
so the upstream velocity equals the upstream <Alfvén speed>. This is the limiting switch-off shock condition.

Solved by gpt-5.6-sol high.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-314/3/d/ii/solution