# Scalar and vector fields

## Main Question or Discussion Point

What is the relation between the flux through a given surface by a vector field? And how does stokes theorem relate to the line integral around a surface in that field

## Answers and Replies

HallsofIvy
The flux of a vector field $\vec{F}$ through surface S is, by definition,
$$\int\int_S \vec{F}\cdot d\vec{S}$$
$$\int_{c} \nabla\times\vec{F}\cdot d\vec{r}$$