An air$-$filled spherical capacitor is constructed with an inner$-$shell radius of $6\mathrm{.}50$ cm and an outer$-$shell radius of $12\mathrm{.}0$ cm$.$

$($a$)$ Calculate the capacitance of the device.

$15\mathrm{.}77$ pF

$($b$)$ What potential difference between the spheres results in a $4\mathrm{.}00-$C charge on the capacitor?

$253\mathrm{.}6$ kV