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)
