  We present an analytical approach for the equilibrium of a self-gravitating
charged fluid embedded in a spherical gravitational and dipolar magnetic fields
produced by a central mass. Our scheme is proposed, as a toy-model, in the
context of gaseous/dusty tori surrounding supermassive black holes in galactic
nuclei. While the central black hole dominates the gravitational field and it
remains electrically neutral, the surrounding material has a non-negligible
self-gravitational effect on the torus structure. By charging mechanisms it
also acquires non-zero electric charge density, so the two influences need to
be taken into account to achieve a self-consistent picture. With our approach
we discuss the impact of self-gravity, represented by the term dt (ratio of the
torus total mass to the mass of the central body), on the conditions for
existence of the equilibrium and the morphology and typology of the tori. By
comparison with a previous work without self-gravity, we show that the
conditions can be different. Although the main aim of the present paper is to
discuss a framework for the classification of electrically charged, magnetized,
self-gravitating tori, we also mention potential astrophysical applications to
vertically stratified fluid configurations.
