= Solution
For an ideal air-gap <parallel-plate capacitor>, neglecting fringing, the <electric field> between oppositely charged plates is $E=\sigma/\epsilon_0=Q/(\epsilon_0 A)$. <Dielectric breakdown> therefore limits the magnitude of the <electric charge> on either plate to
$$
\boxed{Q_{\max}=\epsilon_0 A E_{\rm bd}=(8.854\times10^{-12})(0.03)^2(5\times10^6)\simeq3.98\times10^{-8}\ \mathrm C=39.8\ \mathrm{nC}.}
$$
The two plates carry $+Q$ and $-Q$; the quoted stored <electric charge> is the magnitude on one plate, rather than the net <electric charge> of the whole <capacitor>. The gap does not enter this ideal bound: $C=\epsilon_0 A/d$ and $V_{\max}=E_{\rm bd}d$ make $CV_{\max}$ independent of $d$. Edge enhancement of the <electric field> can lower the practical limit.
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