divergence
Sign in to save500px|thumb|upright=1.75|alt= A vector field with diverging vectors, a vector field with converging vectors, and a vector field with parallel vectors that neither diverge nor converge|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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Divergence is a mathematical measure that tells you whether vectors in a field are spreading out from a point, converging toward it, or flowing parallel to each other. It's calculated by adding up how much the field changes in each direction, and it matters because it helps physicists and engineers understand how quantities like fluid flow, electric fields, and heat distribution behave in space.
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Article
19 sectionsContents
- Physical interpretation of divergence
- Definition
- Definition in coordinates
- Cartesian coordinates
- Cylindrical coordinates
- Spherical coordinates
- Tensor field
- General coordinates
- Properties
- Decomposition theorem
- In arbitrary finite dimensions
- Relation to the exterior derivative
- In curvilinear coordinates
- The divergence of tensors
- See also
- Notes
- Citations
- References
- External links
500px|thumb|upright=1.75|alt= A vector field with diverging vectors, a vector field with converging vectors, and a vector field with parallel vectors that neither diverge nor converge|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}}
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters the volume in an infinitesimal neighborhood of each point. (In 2D this "volume" refers to area.) More precisely, the divergence at a point is the rate that the flow of the vector field modifies a volume about the point in the limit, as a small volume shrinks down to the point.