# Definition:Flux

## Definition

Let $\mathbf V$ be a vector field which acts on a region of space $R$.

Let $S$ be a surface embedded in $R$.

The flux through $S$ is the dot product of $\mathbf V$ with the vector area of $S$.

### Total Flux

Let $\mathbf V$ be a vector field which acts on a region of space $R$.

Let $S$ be a surface embedded in $R$.

The total flux through $S$ is the surface integral over $S$ of the dot product of $\mathbf V$ with the vector area of $S$.