Abstract
Heaviside reformulated the Maxwell equations because he considered that electromagnetic fields and waves have duality. As a result of the reformulation, the Poynting vector was obtained. When the variations of an electromagnetic field propagate in space as waves, this wave is referred to as an electromagnetic wave. The Poynting vector represents the traveling direction of the electromagnetic wave. In this Session, we reexamine electromagnetic fields and waves by focusing on the relationship between the Poynting vector and the duality. According to Wikipedia, no current flows in a vacuum because there are no electrons or electric charges. However, this seems to be incorrect, and the current I(x) given by rotH = I (x) flows in a vacuum. Moreover, a voltage V(x) given by rotE =−V (x) is generated because the magnetic field is the dual of the electric field and the current is the dual of the voltage. As a result, the presence of a coil in a vacuum is expressed by rotE =−V (x) =−∂B / ∂t =− pLI (x) . Namely, the Maxwell equations indicate that “self-induction can occur everywhere in the atmosphere”, as described by Heaviside in the book written by Nahin. Moreover, a capacitor in the atmosphere, including a vacuum, is also given by an equation because it is the dual of the coil. Thus, electromagnetic waves have physical properties of circuit elements including coils and capacitors, which are different from those of lines of forces, such as lines of electric and magnetic forces. The physics of electromagnetic waves is included in classical physics but is different from Newtonian mechanics and uses complex numbers.
