$2.$ A parallel$-$plate capacitor, is made up of two metal plates that each have area $=0\mathrm{.}0252$

and are

separated by a distance d$.$ The capacitance of this capacitor is $4\mathrm{.}4(=4\mathrm{.}4\backslash$times $1012).$

$($a$)$ Determine the distance d$.$

Suppose this capacitor is connected to a $12$ V battery.

$($b$)$ Determine the magnitude of the electric field $||$ between the plates of this capacitor.

$($c$)$ Determine the magnitude of charge on each plate.

$($d$)$ Determine the energy stored in this capacitor.

$($e$)$ If the region between the plates is filled with a material that has a dielectric constant of $3\mathrm{.}5,$ what

does the capacitance become?