 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/8/b/solution

∣\nabla \cdot (\nabla \times F) ∣^{2} = 0 .

Both identities follow by cancellation of equal mixed partial derivatives under the usual smoothness assumptions of vector calculus.

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