Discussion
The divergence of \( \mathbf{A} = (1/r^2)\mathbf{a}_r \) in spherical coordinates, away from the origin, is
Answer: A
The spherical divergence is \( (1/r^2)\partial(r^2 A_r)/\partial r \), and with \( A_r = 1/r^2 \) the bracket is a constant so the derivative vanishes. This is why a point charge gives a field with zero divergence everywhere except at the charge itself.
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