A method is proposed for calculating the mechanical stresses of magnetic and current systems, calculated from the energy density of a uniformly magnetized cylinder. For the calculation, an average in volume demagnetizing factor of the cylinder is introduced, which is proportional to the ratio of the cylinder diameter to its length . It is shown that the demagnetization energy , negligible for a "long" cylinder , ( ), becomes decisive in the formation of stresses at . The radial and axial stresses are investigated in a wide range of ratios.

The presented method is based on the model of an axially magnetized cylinder. The power characteristics of interacting cylinders and / or coils are equivalent if their surface currents are equal. The magnetic system can be composed of cylinders and/or coils. The mutual inductances of the coils follow from the mutual energy of the cylinders, determined through the 3D fields. The fields are calculated using Bessel functions. The features of numerical calculations using the Bessel functions and elliptic integrals are discussed. It is shown that, in calculations using the Bessel functions, there are field oscillations over the end surfaces of the cylinder and local discontinuities of the force graphs appear.