$(10$ pts$)$ Assume we have two very large plates separated by a distance of $50m,$ and we want to create a uniform electric field intensity with a magnitude $E_0=3{10}^4\frac{(V)}{(m)}$ between the plates and pointing from the top plate toward the bottom. Assume no dielectric material between plates $($only air$)$ and zero electric field intensity outside the plates $($i$.$e$.,$ the electric field intensity above the top plate and below the bottom plate is zero$).$ Use Gauss' law to determine the surface charge density required on each plate to achieve the desired electric field intensity.

$(10$ pts$)$ Calculate the potential between the plates in problem $2.$