The parallel plates in a capacitor, with a plate area of $5\mathrm{.}7$ cm$^2$ and an air$-$filled separation of $3\mathrm{.}9$ mm$,$ are charged by a $3\mathrm{.}4$ V battery. They are then disconnected from the battery and pulled apart without discharge$)$ to a separation of $9\mathrm{.}8$ 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 separate the plates.