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

Table of contents
- Solution ii

Solution

If

B_{y 2} = 0

but

B_{y 1} \neq = 0

, tangential momentum continuity in the form

B_{y 2} (A_{2}^{2} - 1) = B_{y 1} (A_{1}^{2} - 1)

A_{1}^{2} = 1

. Since the normal components are positive,

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.

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