1.4.4. Macroscopic Average (Mean) Values

Generalities on the Theory of the Electromagnetic Field and on the Structure of Substance 39

The substance is constituted of molecules that are formed of atoms. According to the Rutherford-Bohr-Sommerfeld atomic model, the substance presents itself in the form of planetary systems, each atom consisting of a nucleus with positive electric charge and of one or more electrons that turn about nucleus around closed orbits.

Concerning the form of a nucleus and of an electron, the simplest proposal is to consider them as being of spherical form. However, this supposition is not satisfactory and it is necessary to use the Quantum Mechanics. Also, there are possibilities of using models that permit to obtain results close to the various ones obtained experimentally [20, p. 64].

The dimensions of nucleus and electrons, in the framework of the simple physical model above, are so small, that in many phenomena, the atomic nuclei and the electrons can be considered of negligible dimensions. Hence, they can be considered as material points or point-like bodies with electric charge and mass. The study of the nucleus structure does not enter into the frame of the present work, and belongs to the domain of Nuclear Physics.

It is useful to be mentioned that, generally, one of the aims of Physics is the determination of the number, repartition and character of the particles charged with electricity which characterize the nature of bodies. Let us give the following example: The derivation of the laws of chemical and physical phenomena, by the aid of interaction laws of particles with electric charge.

The single important exception is represented by the phenomena in which an important function is represented by forces of mechanical nature (gravitation forces, elastic forces, capillary forces, friction forces, etc.) and nuclear forces, because only these forces cannot be reduced to the action of electric charges.

The characterization of the local state of the electromagnetic field in the macroscopic theory may be done by the help of local state quantities of the field: The electric field strength, the electric displacement (electric induction), the magnetic field strength, and the magnetic induction that will be further studied.

1.4.4. Macroscopic Average (Mean) Values

The macroscopic properties have to be described by means of macroscopic quantities. Macroscopic quantities are the quantities obtained by determining the average (mean) values of microscopic quantities for space domains and time intervals that are physically infinitesimal quantities (physically infinitesimal is in French, infiniment petit au sens physique [3, p. 408]). These mean values are called macroscopic average (mean) values.

By a physical infinitesimal domain of space (also called of volume) we understand a domain small enough, from a macroscopic point of view for, within it, the macroscopic quantities show a negligible variation with distance, and at the same time, great enough, from a microscopic point of view. The last condition means that the domain must contain a very great number of particles, i.e., molecules, atoms and elementary particles.

By a physical infinitesimal interval of time we understand a time interval small enough, from a macroscopic point of view for, within it, the macroscopic time-dependent quantities show a negligible variation with time, and at the same time great enough, from a microscopic point of view. The last condition means that the time interval must have the duration much greater than the duration of processes occurring at microscopic scale, i.e., molecular or atomic scale.