  The dynamics of an F=1 spinor condensate in a two-well potential is studied
within the framework of the Gross-Pitaevskii equation. We derive two-mode
equations relating the population imbalances, the phase differences among the
condensates at each side of the barrier and the time evolution of the different
Zeeman populations for the case of small population imbalances. The case of
zero total magnetization is scrutinized in this limit demonstrating the ability
of a two mode analysis to describe to a large extent the dynamics observed in
the Gross-Pitaevskii equations. It is also demonstrated that the time evolution
of the different total populations fully decouples from the Josephson tunneling
phenomena. All the relevant time scales are clearly identified with microscopic
properties of the atom-atom interactions.
