Past exam of the mathematics course of the University of Cambridge / 2014 / ia / Paper 3 / 3A / b / i

F_{i} = f (r) x_{i}

. Summing over the repeated index gives

\partial_{i} F_{i} = f^{'} (r) \frac{x _{i} x _{i}}{r} + f (r) δ_{ii} = r f^{'} (r) + n f (r) .

Here

δ_{ii} = n

\nabla \cdot [f (r) x] = r f^{'} (r) + n f (r) .

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