vektorflux
Vektorflux is a concept in vector calculus describing the net flow of a vector field through a surface, considering the surface's orientation. Given a vector field F defined on a region of space and an oriented surface S, the vektorflux through S is a scalar Φ defined by the surface integral Φ = ∬_S F · n dS, where n is the chosen unit normal to S and dS is the element of surface area.
To compute it when S is parameterized by r(u,v) for (u,v) in a domain D, the differential
For a closed surface S bounding a volume V, Gauss's divergence theorem gives Φ = ∬∬_V (div F)
For surfaces with boundary, related theorems describe other integrals: Stokes's theorem relates the surface integral of
In application, vektorflux measures how much of the field passes through S, with applications in electromagnetism