Some Cases of Explicit Expression of the Intensity of the Resulting Field of Magnets Placed in the Field of External Sources

Formulas are given for calculating the strength of the resulting magnetic field due to magnets with a given magnetization distribution or immersed in a given field of external sources. These are the cases when the calculation using these formulas can be performed by a user who does not have much experience in the field of computational mathematics and programming. Namely, in these cases, the formulas for intensity are mostly expressed in closed form in terms of elementary functions or require the use of one of the standard routines available in the library of any programming language. Such formulas can serve as a reference material as well as for solving relevant problems with suitable real objects or for determining optimal strategies and an optimal set of input parameters when using universal software packages and estimating the error of the results obtained.