$2.[0/2$ Points$]$

SERCP$1116\mathrm{.}7\mathrm{.}0$P$\mathrm{.}051.$

A physicist builds a parallel$-$plate capacitor with adjustable spacing between the plates. When the plates are at their initial separation, the capacitance is $\backslash (4\mathrm{.}50\backslash$mu $\backslash$mathrm$\{$~F$\}\backslash ).$

$($a$)$ At this capacitance, the capacitor is connected to a $14\mathrm{.}00$ V battery. After fully charging, how much energy $($in $\backslash (\backslash$mu $\backslash$mathrm$\{$J$\}\backslash ))$ is stored in the capacitor?

$0\mathrm{.}4$

$\backslash (\backslash$mu $\backslash$mathrm$\{$J$\}\backslash )$

$($b$)$ The battery is then disconnected. Without discharging the capacitor, the physicist then doubles the separation between the plates. At this point, how much energy $($in $\backslash (\backslash$mu $\backslash$mathrm$\{$J$\}\backslash ))$ is stored in the capacitor?