Laplace Equation Relaxation Method

Faculty Commons material developed by Troy Messina - Published August 22, 2023

Description This is a numerical/graphing activities on solving the Laplace Equation. It is designed for the intermediate Electricity & Magnetism course using a text such as Griffiths “Introduction to Electrodynamics”. This activity was derived from Schroeder's (https://physics.weber.edu/schroeder/javacourse/relaxation.pdf) The goal is to calculate the electrostatic potential (or “voltage”) throughout a region that contains electrodes of various shapes, held at various fixed potentials. Students may recall an introductory physics lab in which they measured the voltage throughout a two-dimensional region with various electrodes made of conducting paint. If they did not do this experiment, they can use https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html to simulate the work done in tis activity. This project is the computational counterpart of that experiment. Learning Outcomes: Students develop a deeper understanding of the Laplace equation and its connection to calculating electric potential. Students improve their ability to numerically compute solutions to mathematical and physical problems.

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