SELF

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S.B. Karavashkin and O.N. Karavashkina

5. Causes of variation of propagation velocity of EM wave in the near field

When in the previous item we considered the influence of experimental methods on the pattern of indicated physical process, it would be correct to point also the effect of wave propagation velocity change which has been studied and analysed by many authors, in that number in [16]. We separated an item for this investigation by the following reason. As we will show below, despite this effect is caused just by the dipole type of radiation, at the same time the wave velocity variation in the near field has an objectively physical pattern and does not depend on particular method of measurement, though can be additionally distorted by the imperfect experimental technology.

We will choose some simplified way, concentrating only on the region of normal to the line of dipole charges, since we put the aim to visualise the phenomenology of process, but not to give its comprehensive mathematical analysis. With it we naturally mean that our calculation can be further improved and broadened onto the whole region surrounding the dipole.

To elucidate the cause of EM wave velocity variation in the near field, consider the standard construction shown in Fig. 21.

Fig. 21. Graphical construction to study the EM wave velocity variation in the near field of dipole

We made this diagram in supposition that the EM wave velocity of propagation from each of pulsing sources of dipole is constant and equal to the velocity of EM wave in the far field, i.e. to the light velocity c.

Choose on the axis y two points P₁ and P₂ at which the field strengths are shifted as to each other by the full period of oscillations. With it, naturally, for us in our measurements the distance between the chosen points will be associated with the radiation wavelength, i.e.

At the same time, the wave came to the selected points not from the point O but from the points of charges location - it means, it covered another distance. Noting the symmetry of our problem, to determine the real way which the wave passed from the charges to the selected points, it is sufficient to consider in Fig. 21 only right-hand triangles OP₁B and OP₂B.

From the triangle OP₁B we get

and from the triangle OP₂B

Noting (38), we yield

Transforming (41), we come to the quadratic equation with respect to ':

With strongly positive value of ', the solution of (42) is

Noting that for the half-wave dipole

we yield finally

where