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 $𝐅$, the divergence of $𝐅$ can be written as $\mathrm{div}𝐅$ or $\mathrm{\nabla }\cdot 𝐅$. Here, $\mathrm{\nabla }$ (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

References

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