In this paper, the di erent magnetic  elds on the setting out particle trajectories according to the magnetic  ow attached by the Killing magnetic field are given in Q2 ⊂ E31. The surfaces generated by the Killing magnetic field of the y􀀀magnetic curve are expressed according to asymptotic orthonormal frame field {h, b, y} in Q2 ⊂ E31 and, using Clairaut's theorem the conditions being geodesic on these surfaces of rotation are given. Also, the curvatures and the kinetic energy and angular momentum of the surfaces of rotation formed by y-magnetic curve are examined.