12. Given a material which has the positive charge fixed in this material, the charge density is ρ. The bottom metal is connected to the ground of the system (electric potential = 0). There is a voltage difference V₀ applied between the top and the bottom of the material. This material is infinitely extended in x and y directions. Therefore, the Poisson equation of the electric potential V(z) in this material can be reduced into the differential equation as:

Please evaluate the electric potential V in the middle of this material (z=d/2).
(A) V₀/2
(B) V₀/2 + d²·1/8
(C) V₀/2 - d²·1/8
(D) None of the above

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