Extension of Roth´s method to 2-dimensional rectangular regions containing conductors of any cross-section

Roth´s method for solving 2-dimensional Possion-type field problems was originally restricted to problems in which rectangular conductors had faces parallel to the enclosing boundary region. This method is now extended to problems in which the conductors can have any rectilinear or mathematically definable curved cross-section. It has been shown that such problems can be solved either directly by Roth´s method, or by a combination with the method of superposition. The example treated in this paper is that of an infinitely long conductor of triangular cross-section (as a simple case of nonrectangular cross-section) in a closed rectangular boundary within an infinite iron mass of infinite permeability.