Definition:Flux/Total

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

$F = \ds \int_S \mathbf V \cdot \rd S$

where $\d S$ is an infinitesimal area element of $S$.

Also see

• Definition:Surface Integral

Sources

• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $3$. Line and Surface Integrals: $(2.12)$