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 S2. In this paper, we present Lorentz forces and magnetic curves produced by the Frenet frame {Te, Ne, Be} of the spherical indicatrix of a ruled surface in a magnetic field. We calculate magnetic vector fields of magnetic curves for Te, Ne, Be. 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. © World Scientific Publishing Company.