  A magnetic field is defined by the property that its divergence is zero in a
three dimensional oriented Riemannian manifold. Each magnetic field generates a
magnetic flow whose trajectories are curves called as magnetic curves. In this
paper, we give a new variational approach to studies the magnetic flow
asociated with the Killing magnetic field in a three dimensional oriented
Riemann manifold, And then, we investigate the trajectories of the magnetic
fields called as N-magnetic and B-magnetic curves.
