Magnetic Flux Ruled Surfaces

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 e,t over bar ,g over bar $$ \left\{\bar{e},\overline{t},\overline{g}\right\} $$ 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 over bar $$ \overline{e},\overline{t} $$, and g over bar $$ \overline{g} $$. 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.