EE 341 Matlab Computer Assignment Guide

Ee 341 Matlab Computer Assignment Prof Aaron Scher Guidelines Yo

Work independently to create a PowerPoint presentation, save it as a PDF, and upload it. The presentation should include a title slide with your name, student ID, date, lab name, and class number/title. For the plotting task, you will visualize an electric field described by the vector function \\( \\mathbf{E}(x,y) \\), compute specific values and derivatives at the point (1,1), manually sketch the field, and generate a quiver plot in MATLAB. You will also analytically and numerically compute the electric field due to an infinite line charge at a specified observation point, compare results, and present your MATLAB code and findings accordingly.

Paper For Above instruction

The assignment begins with the visualization of a two-dimensional electric field vector \\( \\mathbf{E}(x,y) \\), which is given by a specific function involving the positions \\( y \\) and \\( \\ell \\). The first step involves manual calculations of the electric field vector \\( \\mathbf{E}(1,1) \\), its divergence \\( \\nabla \\cdot \\mathbf{E} \\), and the divergence of the electric field \\( \\nabla \\cdot \\mathbf{E} \\), all evaluated at the point (1,1). These computations form the foundation for understanding the physical behavior of the field at this point and provide insight into the source distribution that generates such a field.

The subsequent step involves creating a visual sketch of the electric field \\( \\mathbf{E} \\) over a grid spanning from \\( -2 \\) to \\( 2 \\) along both the \\( y \\) and \\( z \\) axes. The sketch, to be presented in slides, should be clear, well-labeled, and easily interpretable, emphasizing the vector directions and magnitudes. To complement the manual sketch, a MATLAB quiver plot will be generated, utilizing the meshgrid and quiver functions. This plot is intended to visually represent the vector field over the specified domain, with MATLAB coding included in subsequent slides.

The assignment then shifts focus to the analysis of the electric field produced by an infinite line charge with a linear charge density of \\( 2 \\) µC/m placed along the z-axis. Analytic expressions for the electric field are given both in cylindrical and rectangular coordinates. Students are required to compute the electric field vector at the point \\( (2,3,4) \\), determining numerical values for the components along respective directions, and expressing the solution explicitly in the slides. This involves calculating the radial vector and the magnitude of the electric field at the observation point, followed by conversion into Cartesian components.

To verify the analytical results, a numerical approximation is to be performed using MATLAB. This involves modeling the line charge as a finite segment, centered at \\( (0,0,4) \\), with a length 100 times the distance from the observation point to the line. The line is subdivided into many small segments, each treated as a point charge, and the electric field contributions from each are calculated and summed. The discrete summation approximation should closely match the analytical solution, and the percent difference between these results will be computed and presented in the slides.

The MATLAB code used for numerical computations is also to be included, illustrating the discretization process, the vector calculations for each segment, and the summation approach. The final slides should showcase the numerical results, compare them with the analytical solution, and provide the corresponding MATLAB code in a clear, readable format.

Overall, this assignment emphasizes the skills of electric field visualization, analytical computation, numerical approximation, and MATLAB programming, designed to reinforce understanding of electromagnetism concepts in a practical computational context. The presentation should be comprehensive, well-organized, and ready for delivery as a PDF file, with proper labeling, clarity, and professional formatting throughout.

References

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