= Solution
Away from the origin, the <electric field> is $E=A r/r^3$, with $r$ here denoting the position vector in the numerator and its <Euclidean norm> in the denominator. The spherical-coordinate formula for <divergence> gives
$$
\boxed{\nabla\cdot E=\frac1{r^2}\frac{d}{dr}\left(r^2\frac A{r^2}\right)=0,\qquad r>0.}
$$
At the origin the <electric field> is singular, so the ordinary <divergence> is undefined there. The equation above must not be extended to the whole space as an ordinary smooth-field identity. Its correct <distributional divergence>, derived in <8/b/ii/solution>, includes the point source.
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