The parallel plates in a capacitor, with a plate area of $6\mathrm{.}90$ cm$?$ and an air$-$filled separation of $3\mathrm{.}20$ mm$,$ are charged by a $4\mathrm{.}20$ V battery.

They are then disconnected from the battery and pulled apart $($without discharge$)$ to a separation of $9\mathrm{.}70$ mm$.$ Neglecting fringing, find

$($a$)$ the potential difference between the plates, $($b$)$ the initial stored energy, $($c$)$ the final stored energy, and $($d$)$ the work required to separate the plates.