Solenoidal vector field

A common way of expressing this property is to say that the field has no sources or sinks.

[note 1] The divergence theorem gives an equivalent integral definition of a solenoidal field; namely that for any closed surface, the net total flux through the surface must be zero: where

automatically results in the identity (as can be shown, for example, using Cartesian coordinates):

The converse also holds: for any solenoidal v there exists a vector potential A such that

(Strictly speaking, this holds subject to certain technical conditions on v, see Helmholtz decomposition.)