On the Physical Nature of the Magnetic-Field Freezing-in Effect in   Collisionless Cosmic Plasmas
  Attention is drawn to a fundamental difference between the physical mechanisms responsible for the magnetic field freezing-in effect in spatially isotropic (collisional) and strongly anisotropic (collisionless) plasmas. (The first case is characteristic of internal regions of the Sun and other stars; the second, for the solar corona, interplanetary and interstellar medium, planetary ionospheres and magnetospheres, cometary tails.) It is shown that particles of a collisionless plasma remain in the same field line during their motion because of the properties of electrodynamic drift which stem from the divergence-free character of the magnetic field and the equipotentiality of the field lines (but not as a result of the appearance of induction currents, compensating variations of the external magnetic flux through a closed contour, as in the case of isotropic conductivity of the plasma). 
Yu. V. Dumin