A Geometric view of Magnetic Surfaces and Magnetic Curves

In the present paper, we approach the magnetic surfaces geometrically. For this aim, we study the problem of constructing a family of magnetic surfaces from a given magnetic field line. We obtain a parametric representation for the surfaces family whose members share the same magnetic field lines and magnetic curves. We investigate the trajectory of charged particles moving related to these surfaces. Moreover, we give various examples of these surfaces and illustrate their figures.