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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.

a) Find the capacitance of this arrangement. Clearly indicate the basic principles and definitions you are using, e.g. the definition of capacitance, the equation that defines the effect of a dielectric on the electric field and so forth.

b) Find the electrostatic force on the dielectric slab when a fixed charge of $\pm Q$ is placed on the two plates of the capacitor. If you cannot do this, for partial credit at least indicate on physical grounds whether the force pulls the dielectric in between the plates (trying to fill the space between them) or pushes it out from between them and explain your reasoning.

Hint: Consider the relation between force and potential energy.