What is the easiest way to understand if the versor normal to a surface is outgoing or ingoing from the surface? (I need this in order to calculate fluxes)
So suppose to have the parametric surface $\mathrm{\bar{r}} : A \subset \mathbb{R^2} \to \mathbb{R^3}$ with $$\mathrm{\bar{r}}(x,y)=\big( \mathrm{r_1}(x,y), \mathrm{r_2}(x,y),\mathrm{r_3}(x,y) \big)$$
If I calculate the normal versor $\bar{\mathrm{n}}$ with the formula, then how to see if it is ingoing or outoging?
My guess would be to see the sign of the dot product $$\bar{\mathrm{n}} \cdot \mathrm{\bar{r}}$$ Since $\mathrm{\bar{r}}$ should be outgoing , therefore if $\bar{\mathrm{n}} \cdot \mathrm{\bar{r}}>0$ then $\bar{\mathrm{n}}$ is outgoing, otherwise ingoing.
Anyway I'm not sure about this. What is the general method to use?