Divergence

In mathematics, divergence is a differential operator that takes a vector field and turns it into a scalar field. In a vector field, each point of the field is associated with a vector; in a scalar field, each point of the field is associated with a scalar. The divergence tells us how much the vector field is "radiating" outward or inward at a point.

Given a vector field ${\displaystyle \mathbf {F} }$, the divergence of ${\displaystyle \mathbf {F} }$ can be written as ${\displaystyle \operatorname {div} \mathbf {F} }$ or ${\displaystyle \nabla \cdot \mathbf {F} }$. Here, ${\displaystyle \nabla }$ (pronounced "del") is the gradient and ${\displaystyle \cdot }$ is the dot product operation.^[1][2][3]

Divergence is used to formulate Maxwell's equations and the continuity equation.

Related pages

• Curl
• Vector calculus