$3.$ The figure shows an electron passing between two charged metal plates that create a $\backslash (92\backslash$mathrm$\{$~N$\}/\backslash )$ C vertical electric field perpendicular to the electron's original horizontal velocity. The initial speed of the electron is $\backslash (2\mathrm{.}8\backslash$times $10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ and the horizontal distance it travels in the uniform field is $4\mathrm{.}2$ cm $.$

a$.$ What direction is the electric field between the plates? Explain.

b$.$ How much time does the electron spend between the two plates?

c$.$ What is its vertical deflection?

d$.$ What is the electron's final velocity $($magnitude and direction angle$)?$

e$.$ How much work is done by the electric force?