The paper constructs the matheamtical model of dynamics of spatial large-scale quasi-geostrophic motions in a rotating layer of ideal incompressible conducting liquid of variable depth with arbitrary values of the magnetic Reynolds number. Our finding can have certain value in astrophysics and geophysics, for example, in the study of processes occurring in stellar interiors and the liquid Earth core; besides, they can be used in evaluating magnetohydrodynamic characteristics of marine environments, in assessing parameters of wave perturbations sources from the electromagnetic field generated by the corresponding hydrodynamic excitement, which contains important information about geophysical characteristics of the shelf zone. This information is relevant for marine geological surveys and studies.