 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/6/b/solution

The vector field has only a vertical component, namely

f (r)

. Its divergence is therefore its vertical partial derivative:

\nabla \cdot [k f (r)] = \frac{\partial f ( r )}{\partial z} = \frac{z}{r} f^{'} (r), r > 0.

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