Directional magnetic and electric vortex lines and their geometries

Abstract

In this study, we introduce directional Fermi-Walker transportation along with the vortex lines of nonvanishing vector fields in the ordinary three-dimensional space. Moreover, we investigate the geometric phase and angular velocity vector (Darboux vector) of vortex lines. Then, we define directional magnetic and electric vortex lines by considering the Lorentz force law and electromagnetic force equation. Finally, we prove a significant relation between directional magnetic and electric vortex lines and angular velocity vector of vortex lines.