Abstract <p>A two-dimensional mathematical model of a magnetoelectric brushless dc motor in polar coordinates is proposed. The model is based on solution of the Laplace equation for the interior of a circular ring by the method of separation of Fourier variables represented as a Dirichlet boundary value problem with respect to the scalar magnetic potential. The Neumann boundary value problem with respect to magnetic induction in a ring is solved by differentiating the magnetic potential along the radial coordinate using Fourier constants of the first Dirichlet boundary value problem. The active parts of the magnetic circuit of the engine are represented as a set of structurally homogeneous circular rings of core yokes, magnets, stator teeth, and an air gap. The unknown Fourier constants—two per ring—are found from the boundary conditions of the magnetic field for the common boundaries of the rings: magnetic potentials and inductions at the boundaries do not undergo jumps. If magnetic sheets of windings are located at the boundaries of the rings, the potential jump is equal to the total current of these sheets.</p>