tokens: H , in which the vertical component of the magnetic field is large, σ c / H . Here, the velocity is the velocity of matter in a vortex. The vortex revolution time is ≃ H /. Apparently, the numerical magnetic viscosity (inversely to the conductivity) in the calculations satisfies this condition. Also, the real conductivity of the turbulent matter is anomalous and significantly less than the classical one. Because of this, the magnetic lines above the disc are directed tangentially to the disc (Teixeira, Avara McKinney 2018 ) and the poloidal magnetic field in magnetosphere is close to radial one due to its strong compression by the plasma pressure of the disc near the central object (Kathirgamaraju et al. 2019 ; Liska et al. 2019 ). Split monopole magnetic field lines directly exit from the vicinity of the central black hole. They are involved into the rotation by the black hole and rotate with an angular velocity of Ω F , which for optimal matching is the half of the angular velocity of rotation of a black hole Ω H , Ω F = Ω H /2 (Blandford Znajek 1977 ). The rotating radial magnetic field excites in the magnetosphere a θ-component of the electric field, E θ , which, by virtue of Faraday’s law, is Here, the element of length d l is taken along the θ direction. We get The relation ( 3 ) looks like a condition ( 1 ) in ideal MHD, where instead of the fluid velocity u the azimuthal rotation velocity appears, u = e φ r sin θΩ F . The electric field ( 3 ) in the magnetosphere arises near the black hole horizon due to its rotation and is transmitted along the radial magnetic field to the magnetosphere, which extends up to the light cylinder surface r = c /Ω F sin θ. The polar field E θ in the magnetosphere is the agent that transfers the black hole rotation to the rotation of plasma of the magnetosphere and, when charged particles move in the polar direction, transfers energy to them. We emphasize here that the polar electric field E θ ( 3 ) is the result the central object rotation, and is not a consequence of MHD, which may not be satisfied in the magnetosphere. This topic is discussed in the section ‘Discussion’. Thus, in the magnetosphere there is an electromagnetic field with components Here, r L = c /Ω F is the natural size of the magnetosphere in the transverse direction. This is the radius of the light cylinder, at which the electric field is compared with the magnetic one. For a spherical distance r , the light surface is at the distance r = r L /sin θ. The value of B 0 is the value of the radial magnetic field at the distance r = r L . At the light cylinder the value of the radial field falls from the value of B 0 near the accretion disc (θ ≃ π/2) to B 0 sin 2 θ. The coefficient α is the ratio of the toroidal magnetic field to the poloidal one at the distance r = r L from the centre. Since the split monopole field and the toroidal field differently depend on the radial distance r , then at ‘small’ distances r α −1 r L the poloidal magnetic
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