The relaxation method is briefly mentioned in Griffiths Sec. 3.1.3 (which made it seem like it...

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The relaxation method is briefly mentioned in Griffiths Sec. 3.1.3 (which made it seem like it can only be used for 2D problems; but it can be applied to 3D problems in general.) It provides an approximate numerical solution to Laplace's equation when given a set of boundary conditions, and is based on one of the properties of the family of functions that satisfies Laplace's equation (i.e., the value of V(r) at any point in space is equal to the average of the values of V around that point). (a) Write a program [in Matlab, Mathematica, Python, C, C++, Fortran, Excel, Labview, etc (it's all up to you)] that will solve Laplace's equation in 2D using the relaxation method. [Include a PDF copy of your numerical code with your submission (with appropriate coding comments/quotes for explanations)]. (b) Using your code, solve V(r) for the space between grounded conducting boundary and a 100-V solid conductor. See Figure 3. Note: This system can be a simple model for concentric electrodes. -100 V 4a $ = 0 Figure 3 (c) From the results of your numerical code, draw equipotential lines in the space between the two elec- trodes. Calculate the electric field vector for each point in space, and draw representative field lines. Briefly discuss your results. 2 (d) Recalculate the potential and electric field line if the horizontal parts of the boundary are grounded, but the left boundary is at a potential of -100 V, and the right boundary is at +100 V. Redraw the equipotential lines and field lines, and briefly discuss your results. The relaxation method is briefly mentioned in Griffiths Sec. 3.1.3 (which made it seem like it can only be used for 2D problems; but it can be applied to 3D problems in general.) It provides an approximate numerical solution to Laplace's equation when given a set of boundary conditions, and is based on one of the properties of the family of functions that satisfies Laplace's equation (i.e., the value of V(r) at any point in space is equal to the average of the values of V around that point). (a) Write a program [in Matlab, Mathematica, Python, C, C++, Fortran, Excel, Labview, etc (it's all up to you)] that will solve Laplace's equation in 2D using the relaxation method. [Include a PDF copy of your numerical code with your submission (with appropriate coding comments/quotes for explanations)]. (b) Using your code, solve V(r) for the space between grounded conducting boundary and a 100-V solid conductor. See Figure 3. Note: This system can be a simple model for concentric electrodes. -100 V 4a $ = 0 Figure 3 (c) From the results of your numerical code, draw equipotential lines in the space between the two elec- trodes. Calculate the electric field vector for each point in space, and draw representative field lines. Briefly discuss your results. 2 (d) Recalculate the potential and electric field line if the horizontal parts of the boundary are grounded, but the left boundary is at a potential of -100 V, and the right boundary is at +100 V. Redraw the equipotential lines and field lines, and briefly discuss your results.