Abstract <p>The solutions of the Laplace equation for a rectangular parallelepiped are considered in the forms of the first and second boundary-value problems using the Fourier method of separation of variables. Based on these solutions, an analytical calculation of electromechanical devices with a radial air gap is proposed, where the yoke, tooth layers, and the air gap of the active region are represented as a set of rectangular parallelepipeds with a width equal to the pole pitch. The associated Fourier constants (two for the elementary parallelepiped) are determined from the characteristics of the magnetic field at the boundaries of the parallelepipeds: the magnetic potentials and magnetic inductions are the same, and, when located at the boundaries of magnetic sheets (MDS of windings), there is a jump in potential equal to the current of the magnetic sheet. Using the proposed method, the magnetic inductions and electromagnetic moment of a superminiature magnetoelectric relay motor are analytically determined in rectangular coordinates.</p>