Two square plates with side length  $\mathcal{l}$ are arranged parallel to each other at distance d. They are charged to a potential difference $V_0$  and isolated from the source. A dielectric with a permittivity  ${\epsilon }_r=2$ whose thickness is d and width is equal to that of the plates is drawn into the space between the plates. The length of the dielectric is greater than $\mathcal{l}$  (figure). The resulting force F acting on the dielectric at distance  $x=\mathcal{l}/2oƒ\frac{\alpha C{V}_0^2}{\beta \mathcal{l}}.$ where  $C=\frac{{\epsilon }_0{\mathcal{l}}^2}{d}.$  Take  $\alpha$ and $\beta$  as minimum integers. Find  $\beta -\alpha .$