$$ An air$-$filled parallel$-$plate capacitor with a $2\mathrm{.}67$mmmm gap width has a capacitance value of $3\mathrm{.}77$FF and holds a charge of $9\mathrm{.}28$CC$.$ The capacitor is not connected to a voltage source.

Part $($a$)$ What is the potential, in volts, across the capacitor?

Part $($b$)$ What is the magnitude, in volts per meter, of the electric field near the center of the gap?

Part $($c$)$ Holding all other parameters constant, the gap between the capacitor plates is filled with an insulating material with a dielectric constant of $5\mathrm{.}28.$ Now what is the potential, in volts, across the capacitor?

Part $($d$)$ Holding all other parameters constant, the gap between the capacitor plates is filled with an insulating material with a dielectric constant of $5\mathrm{.}28.$ Now what is the magnitude, in volts per meter, of the electric field near the center of the gap?