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[tex]

\int\limits_{}^{} {\int\limits_S^{} {\mathop F\limits^ \to } } \bullet d\mathop S\limits^ \to = \int\limits_{}^{} {\int\limits_D^{} {\mathop F\limits^ \to \bullet \mathop n\limits^ \to } } dS

[/tex]

The n vector is an outward unit normal. So does the RHS of the above represent how much 'stuff' is coming out of a surface? Or does it have something to do with what is happening on a surface? The book says that the integral is called the flux of F

*across*S. In many examples, there are little arrows point out of the surface so I'm not sure what the integral is supposed to represent.

Any help would be good thanks.