$(12$ pts$)$ Assume we have a cloud that covers $5k{m}^2$ and rain is falling from the cloud in the absence of any wind $($i$.$e$.,$ the rain falls directly from the cloud toward Earth$).$ Determine the following:

a$)$ Current density due to the rain drops if the charge on each droplet is $2{10}^{-16}C,$ the number of drops per unit volume is $500$drop$\frac{s}{m^3},$ and the drops fall at a rate of $20\frac{m}{s}.$

b$)$ The total current between the cloud and Earth.