Divergence

In mathematics, divergence is a differential operator that associates a vector field with 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.

Given a vector field [math]\displaystyle{ \mathbf{F} }[/math], the divergence of [math]\displaystyle{ \mathbf{F} }[/math] can be written as [math]\displaystyle{ \operatorname{div} \mathbf{F} }[/math] or [math]\displaystyle{ \nabla \cdot \mathbf{F} }[/math], where [math]\displaystyle{ \nabla }[/math] is the gradient and [math]\displaystyle{ \cdot }[/math] is the dot product operation.

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

Divergence Media

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  The divergence of different vector fields. The divergence of vectors from point (x,y) equals the sum of the partial derivative-with-respect-to-x of the x-component and the partial derivative-with-respect-to-y of the y-component at that point:*\nabla\!\cdot(\mathbf{V}(x,y)) = \frac{\partial\, {V_x(x,y)}}{\partial{x}}+\frac{\partial\, {V_y(x,y)}}{\partial{y}}

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Related pages

• Curl
• Vector calculus