The student's question about the amount of charge on a capacitor requires the separation distance between the plates to determine the capacitance and subsequently the charge, which cannot be calculated with the given information alone.
The student is asking about the maximum amount of charge that can be stored on a capacitor without causing a breakdown in dry air, given the electric field limit and the area of the capacitor plates. From the given electric field breakdown strength for air, which is 3.0×106 V/m, and the known relation for a parallel plate capacitor (E = V/d), we can deduce the maximum voltage that can be applied across the plates.
However, to provide the final answer regarding the amount of charge, we need additional information about the separation distance between the plates, as the formula Q = CV (where C is the capacitance of a capacitor, V is the applied voltage, and Q is the charge) also requires the capacitance (C) which is determined by the plate separation and area according to the formula C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between them. Without this distance, we cannot calculate the capacitance or the charge.