Is the Z force Vector Component the same thing as the Poynting vector?

Sir James Jeans' remarks on the Poynting Vector, 1933

This extract is from the classic text, "The Mathematical Theory of Electricity and Magnetism", by Sir James Jeans, published by Cambridge University Press in the fifth edition of 1933. Page 519.

quote..

"The integral of the Poynting Flux over a closed surface gives the total flow of energy into or out of a surface, but it has not been proved, and we are not entitled to assume, that there is an actual flow of energy at every point equal to the Poynting Flux. For instance, if an electrified sphere is placed near to a bar magnet, this latter assumption would require a perpetual flow of energy at every point in the field except the special points at which the electric and magnetic lines of force are tangential to one another. It is difficult to believe that this predicted circulation of energy can have any physical reality. On the other hand, it is to be noticed that such a circulation of energy is almost meaningless. The circulation of a fluid is a definite conception because it is possible to identify the different particles of a fluid; we can say for instance whether or not the particles entering a small element of volume are identical or not with an equal number of particles coming out, but the same is not true of energy."

Jim Ostrowski comments:

The Poynting Vector "points" (pun unavoidable) in the direction of the flow (another word for flux) of electromagnetic energy from point A in space to a point B at some finite distance away. In a rotating magnetic field motor, the rotor component moves in response to a sinusoidal magnetic flux produced by an electric field oscillating in and through the Stator components of the motor. The  magnetic flux in the stator cores is reversing polar directions when evaluating a single core, but rotating polar directions when evaluating all the stator cores cumulatively over the time of a single rotation period. Therefore the Poynting vector, if it could be used at all in describing the full cycle situation, would amount to an arc through the cross section of the Stator beyond the outer diameter of the rotor component, with the AB points at either ends of the arc exchanging places over each half cycle.

 This would mean that  any points along the circumference of the stator assembly designated as, for example, point A as source at one end of the arc and point B as sink 90 degrees away in the case of a two phase (x=sine, Y=cosine) stator, would be arbitrary and phase dependent, because both A(source) and B(sink) would have to exchange positions every half cycle in order to retain their definitions!

Not only that, but the Z-Force Vector value in our description is material or particle dependent as to it's magnitude and effect. Magnets primarily effect ferrous metal structures, but not other kinds. The Poynting Vector is not element dependent as it is ordinarily defined in physics literature.

Therefore:

The Z force Vector Component involved in the study of rotating field electric motor systems is not the same thing as the Poynting vector. If there is another name for the Z-Force vector in the literature, we are not aware of it.

Jim Ostrowski