Bridging Circuits and Fields

CHAPTER 3 Is the Poynting Theorem the Keystone of a Conceptual Bridge between Classical Electromagnetic Theory and Classical Circuit Theory

1. Introduction

At the start of his investigation, the author assumed that a close relationship existed between classical circuit theory (CT) and classical electromagnetic theory (EMT). This assumption is widely shared by specialists in both CT and EMT and is supported by many textbooks and by a large body of scholarly publications.

This assumption was based on a mathematical isomorphism between Steinmetz’s power expression and Poynting’s vector expression. And indeed, in the mathematical formalism of Geometric Algebra (GA), this isomorphism can be expressed as follows:

Steinmetz’s power expression is: ...