Nutations are small variations in the orientation of the Earth’s rotation axis in space. They are caused by the gravitational torque that the Moon, the Sun, and other planets exert on the equatorial bulge. As nutations involve differential rotations between the mantle, fluid core and inner core, the motion of each of these internal regions depends on the coupling between them. In particular, a coupling of a dissipative nature is required to match observations. One possibility is electromagnetic (EM) coupling at the inner and outer core boundaries, the focus of our study. Existing EM coupling models are based on a formulation where the perturbation variables and the equations they must satisfy are defined at local geographic points on the boundary. Here, we show how EM coupling models can be cast under a global formalism, where all variables are expanded in spherical harmonics. This formulation allows a separation of the contribution from the poloidal and toroidal parts of the EM torque, and we show that, under certain conductivity scenarios, this separation is important.