A general formula expressing the density of the magnetic field-aligned current in a partially ionized gas as a function of other physical parameters is derived, and its approximate form, suitable for ionospheric studies, is discussed. Changes of the field-aligned currents in the ionosphere depend on the properties of the vector G representing the total mechanical force acting on a volume of a multicomponent ionospheric 'fluid', dif j⊥, and consequently div j∥, is different from zero if and only if B⋅curl G≠0. Heating of the auroral ionosphere, and a high-altitude enhancement of the atmospheric density associated with it, produces vorticity of the G field that is compatible with the pattern of the field-aligned currents observed above the ionosphere. Variation of E⊥ in the auroral ionosphere is determined from the pattern of j⊥ and from the generalized Ohm law.