Influence of distance between capacitor plates

We have discoverd:$$y(x) \sim V_\text{p}$$For the influence of the capacitor voltage $V_\text{p}$ on the deflection y(x) does the distance d between the two capacitor plates matter. The distance is important for the strength of the electric field between the plates.

Influence of the plate distance on the electric field

The electric field strength $E$ is given by: $$E=\frac{V_{\text p}}{\text d}$$ Because of the distance is non-varying in our experiment it also yields $$y(x) \sim \frac{V_{\text p}}{\text d}\qquad \text{resp.}\qquad y(x) \sim E$$ In the electron deflection tube used in our experiment the distance d between the capacitor plates is \(d=5{.}4\,\rm{cm}\).