Electrostatic fields on PC spreadsheets

Abstract

Electrostatic field solutions involve a large amount of tedious calculation, especially when using coordinate systems more complicated than the standard rectangular, circular, and spherical systems. Many of these calculations can be carried out on a computer, using traditional programming languages such as FORTRAN and BASIC, but this involves writing a program which must be tested and debugged before the results are available. The geometrical nature of the solutions usually requires plotting, and this is normally done as a separate step, whether working on mainframe or personal computers. Spreadsheet packages such as VISICALC, LOTUS 123, or EXEL offer a much faster and simpler alternative to these calculations, since they can accept formulae directly, without programming, and can perform the calculations as soon as the formula is entered. Most versions of these programs also have built-in graphing capabilities, allowing the plots to be seen in a few seconds. In addition, the two-dimensional nature of the spreadsheet allows numerical finite difference methods to be implemented with very little work, and a typical solution of Laplace's equations can be solved in less than 5 min from initial setup to plots of the potential. At each step of the iteration, the recalculated potential is displayed on screen, allowing the operator to get a feel for the convergence of the procedure. Examples of these techniques are used here to illustrate the use of spreadsheets in solution of Laplace's equation and to point out the advantages and disadvantages of this approach to field solutions.