\(\nabla.A\ne\nabla.(-A)\),
refers to a point at the periphery of the spinning field, \(P\) and not at its center \(C\). The flow of \(E\) at the center is reversed when a negative sign is applied.
Strictly speaking,
\(\nabla.A\)
does not represent the effect of spinning \(E\) at point \(P\). Neither does,
\(-\cfrac{\partial E}{\partial t}\)
nor the more familiar,
\(-\cfrac{\partial B}{\partial t}\)
represents the spinning end of a field \(B\) centered at \(C\). It is the negative rate of change with time of \(B\) at a fixed arbitrary point \(P\).
Lunch!
