In this paper, we examine the formation and dynamics of large-scale magnetic structures in the ionosphere of Venus. We show that such structures must be the result of steady state convection of interplanetary field lines into the ionosphere by the small amount of solar wind plasma (≲1--5%) absorbed by the planetary atmosphere below the ionopause, rather than isolated remnants of large fields persisting for long periods without connection ot the solar wind induced current and convection pattern. In particular, we demonstrate that the magnetic diffusion of such structures would result in their dissipation with time scales of 1--10 min, if they were not steady state structures in convective and diffusive equilibrium. It is shown that the equations governing the diffusion of these magnetic structures are similar to those governing diffusion of a gas out of an enclosed chamber with a porous wall, and a simple analog is illustrated. The application of these results to magnetic fields of astrophysical plasmas is discussed.