A parallel$-$plate capacitor has an area A and a plate separation d$.$ The capacitor is connected to a battery $($with voltage AV$).$ Given:

A

d

$2\mathrm{.}0010-*$m$$

$1\mathrm{.}00$ mm

$3\mathrm{.}00-$V

a$)$

b$)$

$[25\%1$ Find its capacitance.

$[25\%]$ Find the charge is on the positive plate when the capacitor is connected to the battery.

$[25\%]$ Calculate the charge density on the positive plate, assuming the density is uniform.

d$)[25\%]$ Calculate the magnitude of the electric field between the plates.

$($You may show your detail procedures that demonstrate your understanding of this scenario to get partial credit even your final answers are incorrect. Otherwise your calculation must be accurate$)$