Boundary Conditions, Integral and Complex Forms of Electrodynamics Equations, Classification of Electromagnetic Phenomena

Abstract

It is known that to precisely solve differential equations with partial derivatives (such equations were discussed in Chap. 1 and should be considered as the base equations for various problems of electromagnetism), we need to formulate the so-called boundary conditions: the values of required solutions of differential equations at definite boundaries. Most often, the boundaries between media of different types are such boundaries for electrodynamics problems. For instance, at electromagnetic wave transfer from the air (where this wave propagates into free space) into, say, the specific dielectric medium, we meet with the necessity of solving the differential equations with partial derivations for the necessity of defining solutions in a two-media (air–dielectric) boundary (interface). The definition of such boundary conditions provides solution unambiguity and, therefore, they are important.