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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. Find:

1. (15 points) the capacitance of this arrangement;
   
2. (5 points) the electrostatic force on the dielectric slab when a potential $V$ is maintained across the capacitor. Does it pull the dielectric in between the plates or push it out from between them?