 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/16/c/ii/solution

(- y, x, 0) \cdot (x, y, z) = - x y + x y = 0

. This vector field is tangent to the sphere everywhere. Therefore its outward flux is

0 .

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