A capacitor with capacitance C is charged to a potential V . What...

A capacitor consists of two plates having equal and opposite charges, $+Q$ and $-Q$.

The total charge enclosed by a closed surface that completely encloses the capacitor is $Q_{enclosed} = +Q - Q = 0$.

According to Gauss's law, the total electric flux through a closed surface is given by $\Phi = \dfrac{Q_{enclosed}}{\varepsilon_0}$.

Since $Q_{enclosed} = 0$, the electric flux through the closed surface is zero.