Three-dimensional large-scale motions of a rotating inviscid incompressible stratified ideal electroconducting fluid in a spherical equatorial latitude belt are studied. The mathematical model of this physical process is a closed system of partial differential equations consisting of hydrodynamic equations, which take into account the Earth rotation and the Lorentz force, and corresponding equations of magnetic dynamics with appropriate boundary conditions. An analytical solution of the system is constructed in the approximation of an equatorial β-plane, which describes propagation of low-amplitude waves.