# EDNE MAY 2015

Electromagnetics Tear Down: The Propagating Plane Wave By Roy McCammon, 3M EMD L&M Laboratory Using the underappreciated fields If you have studied electromagnetic (EM) field theory, you may know that somehow the electric and magnetic fields in a propagating EM wave generate each other to create a self-sustaining wave. This can be proven using vector algebra, partial derivatives and curl. Few people who get that far in their studies can follow the math. Among those who can follow the math, few understand how it works. This article will show with pictures how the fields of a plane wave interact to generate each other with almost no math. To do this, we will introduce two ideas that may be unfamiliar to some readers. The first idea is that ∂D/∂t and ∂B/∂t (the underappreciated fields) are legitimate fields and should be treated as such. In particular, it is useful to depict these fields along with E, H, B and D. The second idea is that a current composed of magnetic monopoles would be associated with the E field in the same way that a current of electrons is associated with the H field. You already know that sending current through a wire coiled into a solenoid shape can create a strong magnetic field inside the solenoid. We will build on that knowledge. But before we do that, we need to define some symbols. Definitions: E Electric Intensity D Electric Flux Density or Electric Displacement Density H Magnetic Intensity B Magnetic Flux Density or Magnetic Displacement Density ∂D/∂t Electric Displacement Current Density ∂B/∂t Magnetic Displacement Current Density The word cause (and related words such as create or generate) will be used in a loose manner. For instance, if we were talking about ohms law, V = I∙R, it might be convenient to say that the current causes the voltage or it might be convenient to say that the voltage causes the current. Given R, current can be derived from voltage or voltage can be derived from current. We will say X causes Y or X creates Y because that is the language we normally use, but we will mean that X and Y have a relationship such that complete knowledge of X mathematically implies complete knowledge of Y and that the result would be the same if X were the actual cause of Y. “Few people who get that far in their studies can follow the math. Among those those who can the math,few understand how it works.” We also need to lightly cover a few unfamiliar topics. • Magnetic Current: Ostensibly, a current composed of moving magnetic monopoles. Just as electric monopoles (electrons for example) in motion constitute an electric current, magnetic monopoles (if they existed) in motion would constitute a magnetic current. There are no magnetic monopoles; but if there were, Maxwell’s equations are readily extensible to include magnetic charge and magnetic currents. Sometimes, when analysing antennas or other EM field problems, the problem can be made easier by transforming the problem to its dual. This can give rise to non-physical magnetic currents. Harrington¹ discusses the generalized Maxwell’s equations and Balanis² discusses how magnetic currents are sometimes used to analyze antennas. Just as electric currents are accompanied by a magnetic (H) field, mag- 29 EDN Europe | MAY 2015 www.edn-europe.com

EDNE MAY 2015