### Bound and trapped classical states of an electric dipole in a magnetic field

### Abstract

In this work, we introduce an approach to facilitate the understanding of concepts about the problem of dipoles in a magnetic field at the senior undergraduate level. We study the classical behaviour of an electric dipole in the presence of an external uniform magnetic field. We obtain equations and constants of motion from the Lagrangian formulation. We find an infinitely periodic effective potential that describes a rotational motion. The problem is not directly separable in relative and centre-of-mass variables, even though we are able to write the energy of the system as a function of only one term, the relative variable. We define another constant of motion, which couples the relative with the centre-of-mass variables. We describe conditions for the 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. Â© 2006 IOP Publishing Ltd.

### Más información

Título según WOS: | Bound and trapped classical states of an electric dipole in a magnetic field |

Título según SCOPUS: | Bound and trapped classical states of an electric dipole in a magnetic field |

Título de la Revista: | EUROPEAN JOURNAL OF PHYSICS |

Volumen: | 27 |

Número: | 6 |

Editorial: | IOP PUBLISHING LTD |

Fecha de publicación: | 2006 |

Página de inicio: | 1315 |

Página final: | 1322 |

Idioma: | English |

URL: | http://stacks.iop.org/0143-0807/27/i=6/a=005?key=crossref.400eb55ccf201d09e157e782edec06f1 |

DOI: |
10.1088/0143-0807/27/6/005 |

Notas: | ISI, SCOPUS |