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To describe the nature of electrical machines’ construction, we have to forget
about the definition of a three-dimensional magnetic field **B** for a
moment.

We will then discover, that elements actually interacting in electrical machines
are magnetic domains of ferromagnetic materials, and elements of a conductor **
∆V** being its volume, through which flows the current, **J** being its
density.

Elements we just mentioned interact with each other through a magnetic field, which results in fact that they are capable of altering their positions, and, as for the magnetic domains, the magnetic moment’s orientation (in case of using soft ferromagnetic).

That means, that the configurative space **M** of such a setup is very
complex, having a structure of subset of a Cartesian product, and considering
the orientation of domain’s magnetic moments, this product includes a group of
rotations **SO(3)**:

Leaving the complex analysis behind, let us assume, that we have found an optimal alignment of magnetic domains in a ferromagnetic against the conductor, through which the electrical current flows, and basing on this fact, we have built an electrical machine of a new type.

Let us notice, that in such a case, the partial derivative of potential energy of a moving element should reach its maximum:

However it turns out, that in case of using soft ferromagnetic we have to implement stabilization of the magnetic domains. Had we not done this, their orientation would have changed due to their interaction with the conductor’s magnetic field, and our construction would have proven to be utterly useless.

That explains the necessity of implementing elements of optimization (in our solutions), which stabilize the magnetic moments orientation of a soft ferromagnetic in rotor by closing its magnetic circuits. Such elements should be placed as near to the rotor as possible to minimize air gap in magnetic circuits.

Let us notice, that the elements of optimization of the stator’s armature can be placed in greater distances from the rotor made of a special type of permanent magnet, because there is no need to stabilize the magnetic moment of the domains.

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