A capacitor with two parallel plates of dimensions $8\mathrm{.}00$ cm x $10\mathrm{.}00$ cm separated by$2\mathrm{.}00$ mm of air is connected to a $24\mathrm{.}0$ V battery. Find $($a$)$ the capacitance of the system,$($b$)$ the charge on one plate and $($c$)$ the electric field inside the capacitor.