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== Verifying the Simulation Results ==
Here we review a simple, approximate, analytical solution of the capacitor problem. Given the large size of the metal plates and their X- and Y-symmetries, one can assume that the electric potential is only a functions function of the z coordinate at the center. The Laplace equation can then be written as:
<math>\nabla^2 \Phi = \frac{d^2\Phi}{dz^2} = 0 </math>
