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

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

then

The converse holds: for any solenoidal v there exists a vector potential A such that . (Strictly, this holds only subject to certain technical conditions on v.)

Examples:

• one of Maxwell's equations states that the magnetic field B is solenoidal;
• the velocity field of an incompressible fluid flow is solenoidal.