= Solution
The <breakdown-limited parallel-plate charge> follows from the ideal <parallel-plate capacitor> relation $Q=CV=(\epsilon_0A/d)(Ed)=\epsilon_0AE$. <Dielectric breakdown> limits the <electric field> rather than the <voltage> independently of separation:
$$
\boxed{Q_{\max}=\epsilon_0(4.0\times10^{-6}\,\mathrm{m^2})(3.0\times10^6\,\mathrm{V\,m^{-1}})
=1.06\times10^{-10}\,\mathrm C\simeq106\,\mathrm{pC}.}
$$
This is the magnitude on either plate, not the sum of both magnitudes. Edge enhancement and fringing are neglected, as in the stated parallel-plate model.
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