The figure below shows a system with two equal capacitors. The capacitance C$=0\mathrm{.}001$mF$,$ d $=1$ mm$,$ and the battery supplies V $=1$ Volt. Initially each capacitor is filled with air.

$1.$ What is the total charge residing in each plate of the $2$ capacitors? Please clearly indicate what is the charge in the top and bottom of each capacitor $($total $4$ answers$).$

$2.$What is the electric field $($direction and magnitude$)$ inside each capacitor.

$3.$What is the effective capacitance of the system?

$4.$While the battery remains connected, we filled the capacitor on the right with a dielectric $=3.$ What is the total charge residing in each plate of the $2$ capacitors $($Please indicate what is the charge in the top and bottom of each capacitor$).$ What is the electric field inside each capacitor?