Some cases of explicit expression of the resulting field strength of magnets placed in the field of external sources

Formulas for calculating of the resulting magnetic field strength of magnets with a given magnetization distribution or given field of external sources are presented. We have collected exactly those cases where a user who does not have much experience in the field of computational mathematics and programming can perform calculations using these formulas. Namely, in these cases formulas for tension are mostly expressed in final form through elementary functions or require the use of one of the standard subroutines available in the library of any programming language. Such formulas can serve both as reference material and for solving corresponding problems with suitable real objects, as well as for determining optimal strategies and the optimal set of input parameters when using universal software packages and assessing the error of the results obtained.