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Consider a capacitor with square plates of area A and seperation d. Two thirds of the space between the plates is completely filled with dielectric material with dielectric constant ε_r1 as shown. The other third is filled with dielectric material with dielectric constant ε_r2.

2170_A capacitor with square plates of area A and seperation d.png

A. Determine the capacitance C_AB.

B. Now the capacitor is connected to an emf V_AB. Determine E^→, D^→, and P^→ inside the dielectrics, bound volume and surface charge densities, as well as the free charge densities on the capacitor plates.

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