Developed by Jordan McDonnell - Published July 16, 2016
|Subject Areas||Electricity & Magnetism and Mathematical / Numerical Methods|
|Level||Beyond the First Year|
|Available Implementation||IPython/Jupyter Notebook|
Students who complete this set of exercises will - be able to use separation of variables to solve Laplace's equation in spherical coordinates for a boundary sphere with given potential (**Exercise 1**), - be able to use separation of variables to solve Laplace's equation in spherical coordinates for a boundary sphere with given surface charge density (**Exercise 2**), - gain familiarity with the Legendre polynomials and their usefulness in physical problems (**Exercises 1 and 2**), - be able to supplement an analytical solution with numerical methods, such as numerical integration (**Exercises 1 and 2**), - and be able to produce and analyze visualizations for the electric potential (**Exercises 1 and 2**).
|Time to Complete||90 min|
These exercises are not tied to a specific programming language. Example implementations are provided under the Code tab, but the Exercises can be implemented in whatever platform you wish to use (e.g., Excel, Python, MATLAB, etc.).
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Credits and Licensing
Jordan McDonnell, "Separation of Variables in Spherical Coordinates," Published in the PICUP Collection, July 2016, https://doi.org/10.1119/PICUP.Exercise.SepVarSpherical.
The instructor materials are ©2016 Jordan McDonnell.
The exercises are released under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license