In the experiments it is erected [1] that at the conductor motion perpendicularly to magnetic force lines in it there is the electric current defined by the Fleming's Right Hand Rule.  Explanations of the causes of existence of this rule miss.

Riddle of behaviour of an electric current.  According to the Unified Тheory the free microvortexes (electrons) in a conductor placed in flow of ether  -- magnetic field are erected by a plane of a vortex across a flow - across of the force lines of magnetic field (What is the magnetic field? and  Core in a solenoid see).

When the conductor is subsequently moved across the flow jets of ether, these jets are bent. Their unidirectional - polarization action (Orientation of the microvortexes see) on microvortices - electrons disappears. The microvortices lose their former stable state. This movement of the microvortex of ether occurs in the ether, which has a viscosity (The ether properties see). The manifestation of the viscosity of the ether leads to the occurrence of a local Return Gravity. The effect of the Return Gravity on the microvortex leads to the unique stable position of these microvortices - until the microvortex (electron) plane coincides with the plane of the curved jet of ether - magnetic field lines  and therefore across the conductor.

From given it is visible, that cross (concerning lines of force of a magnetic field) conductor motion has the same action on electron polarisation, as well as an ether mesovortex of Earth on electrons of Earth (What creates Earth's magnetic field? see).

Thus according to the Unified Тheory the free microvortex (electron) in an ether flow (in an exterior magnetic field) is erected by the vortex plane along the flow fluxion (complanarly axis Х, fig. 50, along of the magnetic force lines). To confirm the uniqueness of the position of the microvortex we will view various orientations of a plane of a vortex concerning axis Х.

   a. If the own transit flow of a microvortex caused by cross gyration of ether in a microvortex (What is the charge? see) is guided on an axis Y and microvortex (electron) together with the body, its containing, translocate on axis Z (on fig. 50 upwards) then the microvortex does not change the orientation concerning axis X. It is caused by that the microvortex translocate forward by the side having the least friction about an exterior flow of ether (because of concurrence of the direction of a longitudinal current in a vortex with the direction of an exterior current) that leads to stability of this motion [27]. At the same time, the own transit flow inside the microvortex due to the viscosity of the ether pumps (moves) the microvortex itself due to the local return Gravity (Return Gravity see) against * the Y axis (Microvortex-pump see) - an electric current arises.

 Fig. 50. The plan to the right-hand rule explanation. 1 – the ether flow
(direction of magnetic lines of force); 2 – a microvortex. 

   b. Other two standings of a microvortex concerning the axes Х (the complanar to axes Y) for the same reason turn a microvortex (electron) in the same standing, as in the item «a», and the microvortex (electron) for the same reason moves against an axis Y.

   c. At a microvortex standing as in the item «a», but turned concerning axis Х on 180⁰, its axial Z motion (upwards on fig. 50) is unstable ([27] see above), since the greatest friction (resistance to its travel) is ahead of a vortex. As a result the vortex is upset on 180⁰ and comes to the stable requirements of the item «a».

As a result all electrons in a body – a conductor move against an axis Y (see * above) – according to a right-hand rule.

Similarly the left-hand rule is explained. Electrons with conductor (their containing) move towards the least viscous friction of an exterior flow of ether about the microvortex ether. 

   *The gained  direction of a motion of an electron is opposite the taken over technical direction of  motion of electric current ([1, p.311, p.348] see above), therefore it corresponds to a right-hand rule.