To find the force between the plates, we consider the electric field produced by one plate acting on the charge of the other plate.

1. Electric Field of a Single Plate: The electric field $E$ due to a single large plane sheet of charge with surface charge density $\sigma = Q/A$ is given by $E = \frac{\sigma}{2\epsilon_0}$ [NCERT Class 12, Chapter 1, Application of Gauss's Law].
2. Force Calculation: The force $F$ exerted on the second plate carrying charge $Q$ (placed in the field of the first plate) is $F = Q \times E$. $F = Q \times \frac{\sigma}{2\epsilon_0} = Q \times \frac{Q}{2A\epsilon_0}$ $F = \frac{Q^2}{2\epsilon_0 A}$
3. Conclusion: The expression for force depends only on the charge $Q$, the area $A$, and the permittivity $\epsilon_0$. It does not contain the separation distance $d$. Therefore, the force is independent of the distance between the plates (provided the distance is small compared to the plate dimensions, maintaining the uniform field approximation).