= Solution
Take the <electric potential> to vanish at infinity. The <distance> from the centre to each <point charge> is half the <diagonal of a polygon> of the <square>, namely $a/\sqrt2$. The <superposition principle> for the <electric potential> therefore gives, for four charges $+q$,
$$
\boxed{V=\frac{1}{4\pi\epsilon_0}\frac{4q}{a/\sqrt2}=\frac{\sqrt2 q}{\pi\epsilon_0a}.}
$$
Strictly, specifying only the \i[magnitude] of each <electric charge> leaves its sign undetermined. For signed charges $q_j$, the general answer is $V=\sqrt2\sum_{j=1}^4q_j/(4\pi\epsilon_0a)$. For example, two positive and two negative charges of equal magnitude give zero <electric potential> at the centre. The boxed result uses the usual interpretation that all four charges have the same positive sign.
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