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Math Formulas > Linear Algebra > Divergence of a Vector Field

Divergence of a Vector Field

The divergence of a vector field is given by:

We define the divergence of a vector field  at a point, as the net outward flux of  per volume as the volume about the point tends to zero.

∇ ∙ A = divA

In Cartesian
∇ ∙ A∂Ax/∂x + ∂Ay/∂y + ∂Az/∂z

In Cylindrical
∇ ∙ A∂(r ∙ Ay)/(r ∙ ∂r) + ∂Aø/(r ∙ ∂ø) + ∂Az/∂z

In Spherical
∇ ∙ A∂(R2 ∙ AR)/(R2∙∂R) + ∂(Aø ∙ sinθ)/(R ∙ sinθ ∙ ∂θ) + ∂Aø/(R ∙ sinθ ∙ ∂ø)

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