This template computes the flux of a vector field through a surface defined over an arbitrary planar region. The field can be specified in its own coordinate system. The surface is given in Cartesian coordinates, either explicitly by using two coordinates as parameters, or parametrically by giving  as functions of two other parameters. The planar domain for the surface can be described by providing its bounding curves in the appropriate parameter space.

VectorCalculus[Flux]

VectorCalculus[SurfaceInt]