Solenoidal vector field

Vector field with zero divergence

In vector calculus and differential equations, a divergence free vector field is a vector field v with divergence zero at all points in the field: ∇ ⋅ v = 0. {\displaystyle \nabla \cdot \mathbf {v} =0.} In electromagnetic theory, a divergence-free vector field is commonly called a solenoidal vector field, while in hydrodynamics it is commonly called an incompressible vector field, and in mathematical physics it is sometimes called an transverse vector field). A common way of expressing this property is to say that the field has no sources or sinks, but one must be careful with this interpretation because there are vector fields without sources or sinks that still have non-zero divergence.

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