# Solenoidal vector field

In vector calculus a solenoidal vector field is a vector field v with divergence zero:

[itex] \nabla \cdot \mathbf{v} = 0.\, [itex]

This condition is clearly satisfied whenever v has a vector potential, because if

[itex]\mathbf{v} = \nabla \times \mathbf{A}[itex]

then

[itex]\nabla \cdot \mathbf{v} = \nabla \cdot (\nabla \times \mathbf{A}) = 0.[itex]

The converse holds: for any solenoidal v there exists a vector potential A such that [itex]\mathbf{v} = \nabla \times \mathbf{A}[itex]. (Strictly, this holds only subject to certain technical conditions on v.)

Examples:

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy