Definition:Flux

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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 $S$.