SELF

74

S.B. Karavashkin and O.N. Karavashkina

It is also commonly known that on the basis of such representation of force lines of power field, EM induction is described as the process of crossing the magnetic field of inducing loop by some loop of force lines, as shown in Fig. 3 [2, p. 248, Fig. 7.19].

Fig. 3. The current l₁ in the loop C₁ produces a definite flux ₂₁ through the loop C₂ [2, p. 248, Fig. 7.19]

"Two loops C₁ and C₂ are fixed in a definite relation as to each other (see Fig. 3). In some way - for example, with the help of battery and rheostat - in the loop C₁ it is produced the current l₁ whose value we can vary. Let B₁(x, y, z) denote the magnetic field which would arise if the current in C₁ had a constant value l₁, and let us denote as ₂₁ the flux B₁ through the loop C₂" [2, p. 248]. Let us interrupt the citation from Purcell and draw our attention that when explaining the process of induction, he compulsorily refers to the "tangible" representation of stationary magnetic field. Should Purcell (or any other author in his place) did not do this excursion into tangible concepts of stationary field, he would have to answer a very inconvenient question of lag of dynamic magnetic field in space. But as we will see further, this question will anyway arise and require from the author to confine himself to infra-low frequencies, in order to avoid the consequences that will inevitably destroy the description of induction process on the basis of flux of magnetic field excited by the loop. Now let us go on with citation.

"Then

where S₂ is the surface bounding the loop C₂. With constant shape and position of two fixed loops, the flux ₂₁  will be proportional to l₁ as follows:

" [2, p. 248].

Here we should stop again and see, (2) is true for stationary magnetic fields, whilst it is applied to dynamic fields, without necessary substantiation. However, as we showed in [1], in dynamic fields not only the field distribution in space is important but also the phase of field variation at each point of space. In this connection, the left-hand part of (2) will not remain constant for different points of loop C₂. Hence, before using this relation, we have to ground it properly phenomenologically and mathematically - and the possibility to ground comes in a great doubt. But let us read on.

"Now suppose, the current l₁ varies in time (notice, only now Purcell really began passing to the dynamic field! - authors), but it varies very slowly, so that the field  B₁  at any point of neighbourhood C₂  and the current  l₁ within the loop C₁  at one and the same instant of time are interrelated just so as they were related in case of direct current (?! - authors). (In order to understand, why such limitation is necessary, imagine C₁ and C₂distanced 10 m from each other and that we increase the current in C₁ twice during 10 nanoseconds! (Actually, what will change with it in phenomenology of process of EM induction? - authors.) ). The flux ₂₁  will vary in proportion to l₁  variation. In the loop C₂ there will appear the electromotive force equal to

" [2, p.248].

And again, let us draw our attention that (2) and (3) are not obviously interrelated; this makes (3) rather an experimental reality having no rigorous substantiation in frames of existing phenomenology.