Simplified Electromagnetic Method for the Analytical Euclidean Modeling of Multiple Electrical Conductors in Arbitrary Directions

The analytical modeling of electromagnetic fields generated by multiple current-carrying conductors is fundamental in power systems, electromagnetic compatibility, and transmission line analysis. Traditional analytical methods often assume conductors aligned with the coordinate system axes, limiting their applicability to arbitrary configurations. This paper presents a novel analytical approach that determines the exact electric and magnetic fields for multiple conductors oriented in arbitrary directions within a Euclidean space, assuming linear, homogeneous, and isotropic media. Unlike numerical methods, such as the Finite Element Method (FEM), which require extensive meshing and domain discretization, the proposed method directly computes field vectors without interpolation or artificial boundary conditions. The applicability of the method is evaluated through four case studies, demonstrating its effectiveness in various configurations, including power transmission lines, communication cables, and grounding systems in homogeneous isotropic media. Additionally, a comparative analysis is performed using a specific case with a known analytical solution, validating the method against FEM-based solvers such as ANSYS Maxwell and FEMM. The results confirm that the proposed approach achieves higher accuracy with significantly lower computational costs.OPEN ACCESS Received: 10/03/2025 Accepted: 09/06/2025 Published: 30/06/2025