An electron is projected with an initial speed $9\mathrm{.}00{10}^5\frac{(m)}{(s)}$ into the uniform field between the parallel plates in$.$ Assume that the field between the plates is uniform and directed vertically downward and that the field outside the plates is zero. The electron enters the field at a point midway between the plates.

$($a$)$ If the electron just misses the upper plate as it emerges from the field, find the speed of the electron as it emerges from the field.

$($b$)$ What is the strength of the electric field?

$($c$)$ What is the potential difference between these two plates?

$($d$)$ What is the capacitance between these plates?

$($e$)$ What net mechanical energy does the electron have at the beginning and end of its trajectory?

$($f$)$ If you were to use an external magnetic field to maintain the original trajectory of the electron, what magnitude and direction would be necessary? You may assume that the magnetic field in the direction of propagation is zero.