THREE PEDAGOGICAL POINTS FOR TEACHING ELECTROMAGNETIC FIELDS TO EE STUDENTS: (Understanding the importance of the distributed systems for circuit theory. Why cannot electromagnetic waves escape a metallic waveguide? Why there must be the returning wave?)

摘要

Firstly, an argument is given for a simple electrical circuit, showing that the "unlimited" use of Ohm's law leads to a contradiction with the theory of relativity, and a wave process has to be considered. The very presence of the electrical voltage v and current i, in a typical resistive dependence v = f(i), is associated with electrical and magnetic fields, or energies, which are inherent for capacitors and inductors. Thus, the common opinion that resistor does not accumulate electrical or magnetic energy is wrong, even the simplest circuits should be analyzed in view of the wave processes, for instance when a DC state is being established. Secondly, giving an introduction to the waveguides, we stress the simplicity with which one can understand, by examining Maxwell's equations that an EM wave can be confined in a metallic waveguide. The conditions for the wave phenomenon to exist, directly observed by Maxwell's equations, is here the key argument. The argument is that for the EM wave to propagate through a conductive wall (cladding), the EM field inside the wall medium has to maintain its wave nature, while the waveguide's metallic tube high conductivity does not allow that. This argument is competitive (or completing) the well-known one in terms of skin-effect. Furthermore, as an important point, we present the question about the sign in a Maxwell equation. Usually, postulating Maxwell's equations as some basic physics equation, and using how to apply them, avoids the question of why the equations are such. We show that putting this sign in focus provides understanding of its origin rooted in correct direction of the energy flow. Finally, we give a very simple argument combining the physics and the mathematics points of view, so that the necessity in the back-traveling wave becomes obvious.