Magnetic spherical indicatrix of a ruled surface

2023/10/14 by Alperen Yıldırım, Emin Kasap, Emi̇n Kasap
Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · #Electromagnetic Scattering and Analysis #Geomagnetism and Paleomagnetism Studies #Scientific Research and Discoveries

paper · doi:10.1142/s0219887824500683

Abstract

The spherical indicatrix of a ruled surface is the image curve of its rulings on the sphere [Formula: see text]. In this paper, we present Lorentz forces and magnetic curves produced by the Frenet frame [Formula: see text] of the spherical indicatrix of a ruled surface in a magnetic field. We calculate magnetic vector fields of magnetic curves for [Formula: see text]. Furthermore, we define magnetic flux surfaces constructed by magnetic vector fields along magnetic spherical indicatrix. We obtain developability conditions for these surfaces. Finally, we give some examples to show magnetic flux surfaces.

Citations

• Magnetic vortex filament flows
• General helices and a theorem of Lancret

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