Solution (source code)

= Solution

Ignoring edge fields, <Gauss's law> gives $E=\sigma/\epsilon_0$ between the parallel plates. Their voltage is $V=Ea=\sigma a/\epsilon_0$, and their charge magnitude is $Q=\sigma s^2$. Therefore
$$
\boxed{C_0=\frac QV=\frac{\epsilon_0s^2}{a}.}
$$