A general solution for the field of polygonal electromagnet

A general solution for the field of a two-dimensional polygonal electromagnet is presented. The solution is applicable to magnetic recording head models of finite size and arbitrary polygonal configuration. It uses a combination of analytic and numerical techniques. Analytic procedures are based on mixed boundary conditions and a succession of conformal mappings starting with the Schwartz-Christoffel (S-C) transformation. A concept of an idealized winding allows any magnetostatic problem to be reduced to an electrostatic problem of two equipotential shims on the plane of conformal mapping. The result of the analytic solution is a parametric formula for the field vector that can be easily obtained for any model by an inspection of its configuration. This formula contains S-C constants and parameters of unknown values. These difficulties are resolved by numerical procedures