1.3. Physical Quantities. Laws and Theorems

36

GeneralTheoryoftheElectromagneticField

n n n

n

S

S

a b c

Fig. 1.2. The reference directions to the calculation of fluxes for: a – closed surface; b – open surface; c – manifold open surface.

surfaceboundedbyacurveformingseveralnearloops(thecaseofahelix).Thesurface is a helical one.

Weshallrecallthegenerationofahelicalsurface.Considerastraight-linesegment havingoneendatanypointononeaxiswithwhichthesegmentformsaconstantangle. Letthesegmentrotateabouttheaxis,andsimultaneouslythepointrepresentingtheend abovetomovealongtheaxiswithsegmentsproportionaltothearcofrotationofthe segment.Thecurvedescribedbyeachpointofthesegmentwillbeahelix.Thesurface described by the segment will be a helical surface.

Inthecaseofthehelicalsurface,itfollowsthatthisfluxis,infact,equaltothesumof fluxes through every loop.

Thefluxcorrespondingtoallloopsisreferredtoaslinkedfluxor flux-linkage.The flux through a single sheet is referred to as flux-turn.

Eachtubeoffieldlinescontainingafluxequaltotheunitmaybeassociatedwitha centrallineoffield.Thislinemaybereferredtoasunitfieldlineorunitfluxline.Then, thefluxthroughanysurfacewillbeequaltothenumber representingthealgebraicsum (i,e.,takingintoaccountthesenseofthelines)oftheunitfieldlinesthatpassthroughthe surface.

1.3. PHYSICALQUANTITIES.LAWSANDTHEOREMS.

The characterization of physical states and phenomena is achieved by means of physicalquantities.Adetailedanalysisreferringtophysicalquantitieshasbeenmadein

Generalities on the Theory of the Electromagnetic Field and on the Structure of Substance 37

several works [1], [8], [11], [21], [22]. Further on, some principal aspects will be explained.

A kind of a physical quantity (in French, espèce de grandeurs physiques) is a class of physical properties susceptible of quantitative determination. For defining the kind of a physical quantity, it is necessary to know the measuring procedure and the unit of measure. The choice of the unit of measure is arbitrary. As examples, the following three kinds of quantities utilized in electromagnetism will be given: Electric charge, electric field strength, magnetic field strength.

A kind of physical quantity characterizes a common property of the elements (objects) of a set of physical objects. To identify a common property of a set of physical objects, it is necessary that a relation of order should exist between these objects.

A measure procedure is a repeatable experimental operation, by which, to each physical quantity it is possible to associate a mathematical quantity called value or magnitude in respect to a physical quantity termed unit.

According to the manner of introducing, the kinds of physical quantities can be divided into the following ones: Kinds of primitive quantities and kinds of secondary (derived) quantities (in French, espèces de grandeurs primitives et espèces de grandeurs secondaires ou dérivées), also termed primitive and secondary (derived) quantities, respectively (in French, grandeurs primitives et, respectivement, grandeurs secondaires ou dérivées). The kinds of secondary (derived) quantities can be defined by means of other ones supposed as being known, hence introduced previously. The kinds of primitive quantities have to be introduced directly, by experimental way, and described by the measurement procedure, because they can no more be defined by means of quantities introduced previously.

In electromagnetism, apart from the primitive quantities of mechanics (length, time, mass, force), a series of new primitive quantities is necessary for characterizing from an electromagnetic point of view the state of bodies and of the electromagnetic field.

A system of units contains fundamental and derived units (in French, unités fondamentales ou de base et unités dérivées). The fundamental units have to be determined directly, experimentally (e.g., the metre). The derived units are derived by using the fundamental units (e.g., the square metre). The fundamental units must not be those of the primitive quantities, but those of the quantities that frequently appear in practice.

The laws express relations that are essentially necessary and repeatable between phenomena. In physics, laws are called the relations that express the most general knowledge on the phenomena of a research domain. They reflect the objective properties (of phenomena) that cannot be deduced by logical analysis (in the framework of the respective research field) from more general relations. The laws are established by the generalization of a great number of experimental results. In the theory of the electromagnetic field, there are general laws and material laws also called constitutive laws. The material laws differ from the general ones by the fact that they contain in their expression quantities specific to various materials, called material quantities.

The relations that can be deduced by logical analysis from other more general ones, and finally from laws, are called theorems.

It is useful to mention that there are relations that, at the time at which they were established, had law character but subsequently, after the progress of science, more general relations were discovered and the first ones could be derived or have represented