The drift velocity VB of magnetic fields relative to the fluid is obtained by solving the motions of many kinds of charged particles. Any closed curve moving with vB has a constant magnetic flux. This velocity contains the effects of both plasma drift and Joule dissipation. At the hydrogen density |nH10¹¹\,cm⁻³|, υB is at least 10 times smaller than the free-fall velocity uf, and then field dissipation is inefficient. At |nH10¹²\,cm⁻³| and temperature |T<10³\,K| where thermal ionization is inefficient, however, υB exceeds uf unless the characteristic curvature radius of field lines is much greater than the characteristic length of the cloud. In such a situation, charged grains are more abundant than ions, and the field decays mainly through Joule dissipation. Thus the magnetic field is decoupled from the gas and only nearly current-free fields can exist in a part of the cloud with |nH10¹²\,cm⁻³\,and\,\,T<10³\,K|.
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Nakano et al. (1986) studied this question.