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I. Finite Difference Method for Numerical Solution of Laplace's Equation - Square Coaxial Cable Consider an air-filled coaxial cable with conductors of a square cross section. Let the cross-sectional dimensions of the cable be a-1 cm (inner conductor), b-3cm (outer conductor). The cable is charged by time-invariant charges, and the potentials of the conductors, V- V and V--1 V FD direct solution: Perform FD analysis of the coaxial cable by directly solving the system of linear algebraic equations with potentials at interior grid nodes as unknowns. Plot the results for the distribution of the potential in the space between the conductors and calculate the capacitance per-unit-length of the cable, taking the grid spacing to be d-a/N and the tolerance of the potential -le-8 V, where N-5, 10, 20. 1. 2. FD iterative solution 1: Perform FD analysis of the coaxial cable using relaxation technique. Compare results to the ones obtained by direct solution 3. FD iterative solution 2: Perform FD analysis of the coaxial cable using over-relaxation technique. Compare results to the ones obtained by direct solution and iterative solution 1. I. Finite Difference Method for Numerical Solution of Laplace's Equation - Square Coaxial Cable Consider an air-filled coaxial cable with conductors of a square cross section. Let the cross-sectional dimensions of the cable be a-1 cm (inner conductor), b-3cm (outer conductor). The cable is charged by time-invariant charges, and the potentials of the conductors, V- V and V--1 V FD direct solution: Perform FD analysis of the coaxial cable by directly solving the system of linear algebraic equations with potentials at interior grid nodes as unknowns. Plot the results for the distribution of the potential in the space between the conductors and calculate the capacitance per-unit-length of the cable, taking the grid spacing to be d-a/N and the tolerance of the potential -le-8 V, where N-5, 10, 20. 1. 2. FD iterative solution 1: Perform FD analysis of the coaxial cable using relaxation technique. Compare results to the ones obtained by direct solution 3. FD iterative solution 2: Perform FD analysis of the coaxial cable using over-relaxation technique. Compare results to the ones obtained by direct solution and iterative solution 1