Abstract: This paper is intended to calculate the magnetic field of a line electric current in the infinite deep trough imited by a ferromagnetic substance by using Schwarz-Christoffel transformations on the coordinate system of the complex number and mirror image method. We obtain the magnetic potential arrow distribution and magnetic induction line equation. The magnetic induction line map is plotted by using the software MATLAB

Key words: ferromagnetic substance, limitless deep trough, line electric current, Schwarz-Christoffel transfor- mations, mirror image method, magnetic potential arrow