Summary form only given. We study the effect of the ambipolar diffusion (joint transport of magnetic flux and charged particles relative to neutral particles) on the long-term evolution of a magnetic field one dimensional configuration. Our system is a weakly ionized plasma in which neutral and charged particles can be converted into each other through nuclear beta decays or ionization-recombination processes. We show numerically that ambipolar diffusion tends to spread out the magnetic flux, but, contrary to the normal Ohmic diffusion, it produces sharp magnetic-field gradients with associated current sheets around those regions where the magnetic field is weak. These results could have applications in explaining relevant processes promoting the magnetic field evolution inside neutron stars (particularly magnetars), magnetic field evolution in the interstellar medium and the loss of magnetic flux from collapsing molecular cloud cores.