Editing Solenoidal vector field (section)

{{Short description|Vector field with zero divergence}}
[[File:Solenoidal vector field 1.svg|thumb|250px|An example of a solenoidal vector field, <math>\mathbf{v}(x, y) = (y, -x)</math>]]
In [[vector calculus]] a '''solenoidal vector field''' (also known as an '''incompressible vector field''', a '''divergence-free vector field''', or a [[Helmholtz decomposition#Longitudinal and transverse fields| '''transverse vector field''']]) is a [[vector field]] '''v''' with [[divergence]] zero at all points in the field:
<math display="block"> \nabla \cdot \mathbf{v} = 0. </math>
A common way of expressing this property is to say that the field has no [[sources and sinks|sources or sinks]].<ref group="note">This statement does not mean that the field lines of a solenoidal field must be closed, neither that they cannot begin or end. For a detailed discussion of the subject, see J. Slepian: "Lines of Force in Electric and Magnetic Fields", American Journal of Physics, vol. 19, pp. 87-90, 1951, and L. Zilberti: "The Misconception of Closed Magnetic Flux Lines", IEEE Magnetics Letters, vol. 8, art. 1306005, 2017.</ref>