Using the experiment we determined that for the electron deflection $y(x)$ in a uniform electric field of a plate capacitor the following relations are valid:
$y(x) \sim V_{\text p}\qquad $ (deflection proportional to plate voltage)
$y(x) \sim \frac{1}{V_{\text a}}\qquad $ (deflection antiproportional to acceleration voltage)
$y(x) \sim x^2\qquad $ (deflection proportional to the square of the length x in the plate capacitor - parabolic shape)
With the experimental determined preliminary factor $\frac{1}{4}$ the electron trajectory is: $$\bbox[5px,border:2px solid red] {y(x)=\frac{V_{\text p}}{4\cdot \text{d}\cdot V_{\text a}}\cdot x^2}$$So the trajectory is a stretched or compressed parabola. A more physical derivation of this formula is given in the next chapter.
Hypotheses
Experiment
