homework_5 - perpendicular to the planes WHat is the...

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ELECTRODYNAMICS PROBLEM SET 5 due March 2 nd , before class Problem 1: Relaxation method Implement the relaxation algorithm described in class to find the potential inside a region with the shape as in the figure. The top edge is kept at φ = V and the other borders at φ = 0. Estimate the error in your answer. Can you achieve a 1% precision at the center of the upper left square? (you can use units where V = 1, L = 1). L/2 L/2 L Problem 2: Dipole layer Two parallel infinite planes are charged with charge densities σ and - σ . Plot the potential along a direction
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Unformatted text preview: perpendicular to the planes. WHat is the potential drop across both planes? hint: this is as trivial as it looks Problem 3: Infinite cylinder Consider an cylinder with radius a and length L . The curved surface and the bottom z = 0 face of the cylinder are kept at potential φ = 0. The top of the cylinder is z = L is kept at φ = V . Compute the potential inside the cylinder. Use the properties of these Bessel function you may need without proof....
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