Trapped and Bound Classical States of an Electric Dipole in Magnetic Field

In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic effective potential that describes a rotational motion. The problem is not directly separable in relative and center of mass variables; even though, we are able to write the energy of the system as a function of an only term, the relative variable. We define another constant of motion, which couples the relative with the center of mass variables. We describe conditions for bound states of the dipole. In addition, we discuss the problem in the approximation of small oscillations. Finally, we explore the existence of a possible family of trapped states in a region of the space where there are no classical turning points.