Chapter 5: Electroquasistatic fields from the boundary value point of view

author: Markus Zahn, Center for Future Civic Media, Massachusetts Institute of Technology, MIT
recorded by: Massachusetts Institute of Technology, MIT
published: Oct. 10, 2008,   recorded: September 2005,   views: 3659
released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)

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5.0 Introduction

5.1 Particular and homogeneous solutions to Poisson's and Laplace's equations

  • Superposition to satisfy boundary conditions
  • Capacitance matrix

5.2 Uniqueness of solutions of Poisson's equation

5.3 Continuity conditions

5.4 Solutions to Laplace's equation in Cartesian coordinates

5.5 Modal expansions to satisfy boundary conditions

5.6 Solutions to Poisson's equation with boundary conditions

5.7 Solutions to Laplace's equation in polar coordinates

5.8 Examples in polar coordinates

  • Simple solutions
  • Azimuthal modes
  • Radial modes

5.9 Three solutions to Laplace's equation in spherical coordinates

5.10 Three-dimensional solutions to Laplace's equation

  • Cartesian coordinate product solutions
  • Modal expansion in Cartesian coordinates
  • Modal expansion in other coordinates

5.11 Summary

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