energy - Capacitor with a dielectric with only one plate / with one plate moving

I was wondering how a capacitor like the one in the picture below works. The length of the plates is L and their width is b (parallel to the z axis). The distance between the plates is d. The whole space between the plates is filled with a dielectric of relative permittivity ε_r. At the beginning the capacitor has charge Q. (picture a)

The lower plate is fixed to the ground but the upper one can be moved. Suppose it has moved a distance x along the x axis (picture b).

I was wondering what happens to the charge in this situation (assuming it is conserved). What are the charges Q1, Q2, Q3, Q4? What is the energy of this capacitor? I want to use the equation for the energy (derivating it with respect to x) to find the force stopping the movement of the upper plate (In my original problem, the capacitor is situated on a plane and the upper plate slides down due to the force of gravity).

The part with charge Q3 doesn't have any input, does it? Should I somehow include the part with charge Q4, even though there is only one plate there? I know there is a charge induced in the dielectric here and I can find it knowing Q4 but I don't know how I should treat this part of the capacitor calculating the energy.

EDIT: We assume that d << L and d << b. Also: x >> d but x < L (in fact it will be x < L/2 in the original problem so that the upper plate won't rotate on that plane). For space outside the dielectric ε_r = 1.