Regarding the Earth and a cloud layer $800$ m above the Earth as the plates of a parallel plate capacitor of the Earthcloud layer system. Assume the cloud layer has an area of $1\mathrm{.}00$ km$2$ and the air between the cloud and the ground is pure and dry. Assume charge builds up on the cloud and on the ground until a uniform electric field of $3\mathrm{.}00$ x$106$ N$/$C throughout the space between them makes the air breakdown and conduct electricity as a lightning bolt. $($a$)$ Calculate the capacitance of the Earthcloud layer system. $($b$)$ What is the maximum charge the cloud can hold?