This template computes the flux of a vector field through a surface defined over a disk. The field can be specified in its own coordinate system. The surface is given in Cartesian coordinates $x$, $y$, $z$, either explicitly or parametrically. Thus, the surface parameters can be two of the coordinate variables, or all three coordinates for the surface can be functions of two other parameters. The disk, specified by giving its center and radius, is in the space of the parameters. Thus, if the surface is parametrized as $x$($u$, $v$), $y$($u$, $v$), $z$($u$, $v$), the support of the surface is a disk in the $\mathrm{uv}$-plane, not the $\mathrm{xy}$-plane.

VectorCalculus[Flux]

VectorCalculus[SurfaceInt]