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 
Learning Objectives 
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.).
Download Options
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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.
DOI: 10.1119/PICUP.Exercise.SepVarSpherical
The instructor materials are ©2016 Jordan McDonnell.
The exercises are released under a Creative Commons AttributionNonCommercialShareAlike 4.0 license