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 $\mathbf {F}$, the divergence of $\mathbf {F}$ can be written as $\operatorname {div} \mathbf {F}$ or $\nabla \cdot \mathbf {F}$. Here, $\nabla$ (pronounced "del") is the gradient and $\cdot$ is the dot product operation.

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

Related pages

• Curl
• Vector calculus