An air filled parallel plate electrostatic actuator is shown in the figure. The area of each capacitor plate is $100 \: \mu \mathrm{m} \times 100 \: \mu \mathrm{m}$. The distance between the plates $d_{0}=1 \mu \mathrm{~m}$ when both the capacitor charge and spring restoring force are zero as shown in Figure (a). A linear spring of constant $k=0.01 \mathrm{~N} / \mathrm{m}$ is connected to the movable plate. When charge is supplied to the capacitor using a current source, the top plate moves as shown in Figure (b). The magnitude of minimum charge $(Q)$ required to momentarily close the gap between the plates is ___________ $\times 10^{-14} \mathrm{C}$ (rounded off to two decimal places).
Note: Assume a full range of motion is possible for the top plate and there is no fringe capacitance. The permittivity of free space is $\varepsilon_{o}=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}$ and relative permittivity of air $\left(\varepsilon_{r}\right)$ is $1$.
