# Electrostatics - System of parallel plates

For a system of $n$ parallel metal plates bearing charges $q_1, q_2,\dots, q_n$, why it is so that the facing surfaces of the plates bear equal and opposite charges?

How do we prove that?

Thus $$\phi_{net}=0$$ but from gauss law$$\phi_{net}=q_{enclosed}/\epsilon$$ thus its only possible when q enclosed is zero. Which is further only possible for pair of equal and opposite charges.