Problem 7. A A X- You are given a square parallel plate capacitor of side L and plate separation d and a slab of dielectric material with relative dielectric permittivity er that exactly fills the volume between the plates if fully inserted. At the moment, however, the slab is inserted only a distance x. The capacitor has a constant free charge Qo on it. a) Find the potential energy of the partially filled capacitor, as a function of Qo, L, d, co, Er and x. b) Is the potential energy minimal when the dielectric slab is fully inserted or fully re- moved? Explain why. c) By using du Fx dx find the force on the partially inserted dielectric slab. Does the force pull the dielectric slab in (to fill the plate volume) or does it push it out from between the plates? d) Draw a simple picture involving the probable bound charge distribution on the partially inserted dielectric slab that physically explains this force