Maxwell's Equations Beyond the Cartesian, Cylindrical and Spherical Coordinate System

Roberto Armenta

The Edward S. Rogers Sr. Department of Electrical and Computer Engineering (Electromagnetics)

Abstract:

Electrical engineers receive most of their training in electromagnetic theory using three coordinate systems: Cartesian, cylindrical and spherical. The conventional justification for sticking to such pedagogical strategy is that it allows students to understand basic physical concepts without having to resort to complicated mathematics.  While there is truth to this argument, learning electromagnetic theory using only three coordinate systems can introduce undesirable biases in the way coordinate systems are used and understood. A particularly good example can be found in the numerical techniques that are commonly used to solve Maxwell's equations. There, the role of coordinate systems is often completely misunderstood. When pursuing a numerical solution, hanging on to the Cartesian, cylindrical and spherical coordinate systems can be strongly counterproductive. This is true even in problems that contain nothing but rectangular, cylindrical and spherical objects! To come up with the best strategy for solving a given problem numerically, it is necessary to learn how to view and formulate the laws of electrodynamics in a manner that is independent of the coordinate system being used. In this presentation, such a formulation of Maxwell's equations is given. This formulation can be exploited not only to improve numerical algorithms but also to gain new physical insights into the operation of many microwave and photonic devices.

Biography:

Roberto is a PhD student in the electromagnetics group.