A parallel plate that has an area of $13\mathrm{.}5$ cm$2$ with the $2$ plates being $8\mathrm{.}9$ mm apart, is hooked up to a $9\mathrm{.}0$ V battery.

a$.$ What is the capacitance of the capacitor?

b$.$ What is the charge on the capacitor?

c$.$ How much potential energy is stored in the capacitor?

d$.$ What is the electric field between the plates?