Suppose that $F$ is a function field of a smooth geometrically connected curve $C$ over $\mathbb{F}_q$. So $F$ is some function field with constants $\mathbb{F}_q$. We could instead look at $C$ over some larger finite field $\mathbb{F}_{q^n}$ and get a new corresponding function field, say $F'$ (which I believe is just $F \otimes_{\mathbb{F}_q} \mathbb{F}_{q^n}$).
How are the genera of $F$ and $F'$ related? That is, if $F$ has genus $g$ what is the genus of $F'=F \otimes_{\mathbb{F}_q} \mathbb{F}_{q^n}$?