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A parallel plate capacitor has cross sectional area $A$ and separation $d$. A dielectric material with dielectric constant $\kappa$ of thickness $d$ and area $A$ fills the space in between as shown.

Suppose a potential $V$ is connected across this capacitor. Find the electric field inside the dielectric, the free charge (and hence the capacitance), and the bound charge on the surface of the dielectric. Show all work!