Magnetic spherical indicatrix of a ruled surface

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.