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The Use of Spreadsheets in Teaching Boundary-Value Problems in Electromagnetics

Abstract

Electromagnetics is arguably one of the most challenging courses in any electrical engineering curriculum. A solid foundation in vector calculus and a good intuition based on physical grounds are the normal requirements for a student to successfully complete this course. This paper presents a simple, yet powerful approach to introducing boundary-value problems arising in electrostatics. The principles of electrostatics find numerous applications such as electrostatic machines, lightning rods, gas purification, food purification, laser printers, and crop spraying, to name a few.

This paper focuses on the use of spreadsheets for solving electrostatic boundary-value problems. Sample problems that introduce the finite difference and the finite element methods are presented. The geometries included in the problems are sufficiently nontrivial for hand calculation or analytical solution, but reasonably manageable using spreadsheets. Although specialized software is available for this purpose, oftentimes such sophistication tends to obscure the mathematical underpinnings of the solution methods. Spreadsheets offer a transparent

numerical methods for solving boundary-value problems.

1. Introduction

Many phenomena arising in science and engineering are modeled by partial differential equations (PDEs). In such cases the quantity of interest (e.g., temperature, potential, or displacement) is a function that depends on more than one variable (typically, space variables x, y, z and the temporal variable t). among the most common PDEs that undergraduate engineering students will encounter. The usual practice is to introduce the student to the analytical solution of these equations via the method of separation of variables. Under the assumption of linearity, the method naturally leads to the formulation of solutions as Fourier series expansions.

Treatment of PDEs and boundary-value problems (BVPs) may be found in many standard books.1 4 Reference 1 provides a very accessible presentation of the topic, while references 2 through 4 provide a more concise presentation geared toward compendium courses in engineering mathematics. This paper will not expound the theories that provide the mathematical underpinnings of PDEs; instead, the paper emphasizes on numerical solutions of PDEs and suggests implementations through spreadsheets.

This paper focuses on some numerical methods for solving PDEs; in particular, the finite difference and the finite element methods are presented in the context of problems arising in electrostatics. Much of the development of these methods will follow those found in electromagnetics books.5 The examples presented in this paper include geometries that are

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Lau, M., & Kuruganty, S. (2010, June), The Use Of Spreadsheets In Teaching Boundary Value Problems In Electromagnetics Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--15681