Which velocity does the electrons have when leaving the electric field?

In a previous chapter we have seen, the the electrons are not accelerated in x-direction. They move with constant speed in x-direction within the plate capacitor.
We have also seen that the electrons are accelerated in y-direction. So the electron velocity in y-direction changes while moving through the plate capacitor.

Tasks:

Electrons enter an plate capacitor with \(v=4{,}2\cdot 10^{7}\,\rm{\frac{m}{s}}\). The capacitor is \(l=0{,}12\,\rm{m}\) long and the distance between the plates is \(d=0{,}06\,\rm{m}\). Plate Voltage is \(V_{\rm{p}}=2000\,\rm{V}\), the elementary charge is \(e=1{,}6\cdot 10^{-19}\,\rm{C}\) and the mass of an electron ist \(m=9{,}1\cdot 10^{-31}\,\rm{kg}\).
Electron velocity when leaving the plate capacitor
equation of motion in y-direction
$$\begin{equation}y(t)=\frac{1}{2}a_y\cdot t^2\end{equation}$$
$$\begin{equation}v_y(t)=a_y\cdot t\end{equation}$$
$$\begin{equation}a_y(t)=\frac{F}{m}=\frac{V_{\text p}\cdot e}{m\cdot \text{d}}\end{equation}$$
  • Calculate the acceleration \(a_y\) acting on the electrons inside the plate capacitor in y-direction.
  • Calculate the electron velocity \(v_y\) when leaving the plate capacitor.
  • Calculate the resultant velocity \(v_{\rm{res}}\) of the electrons when leaving the plate capacitor.