Magnetic flux ruled surfaces. (22nd November 2022)

• Record Type: Journal Article
• Authors: Bayram, Ergin; Güler, Fatma; Kasap, Emin
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 5(2023)
• Page Start: 5989
• Page End: 6001
• Publication Date: 2022-11-22
• Subjects: flux surfaces -- magnetic curves and surfaces -- ruled surfaces -- striction curve; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8884
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : There is a unique curve called striction curve that is not present on a surface except a ruled surface. This curve is defined as the shortest distance with the help of a common perpendicular line between two adjacent rulings. In this work, we present Lorentz forces and magnetic striction curves produced by the geodesic Frenet frame ē, t ¯, g ¯ $$ \left\{\bar{e}, \overline{t}, \overline{g}\right\} $$ on the striction curve of the ruled surface defined by the spherical indicatrix curve in a magnetic field. We calculate magnetic vector fields of magnetic striction curves for e ‾, t ¯ $$ \overline{e}, \overline{t} $$, and g ¯ $$ \overline{g} $$ . Furthermore, we define magnetic flux surfaces constructed by magnetic vector fields along magnetic striction curves. We obtain developability conditions for these surfaces according to their curvature functions. Finally, we give some examples about magnetic flux surfaces.