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A parallel plate capacitor is constructed from two square conducting plates of with an area of $A$, separated by a distance of $d$. An insulating slab of thickness $d$ and a dielectric constant $\kappa$ is inserted so that it half-fills the space between the plates as shown. Find:

1. The capacitance of this arrangement;
   
2. The electrostatic force on the dielectric slab when a the capacitor carries a total charge (fixed) $Q_0$ on the top plate and $-Q_0$ on the bottom plate.
3. For extra credit, would the direction of the force be the same if a constant voltage $\Delta V$ were applied across the plates? Indicate why if you try to answer this one.