ABSTRACT
The traditional generalized Ohm’s law in MHD (Magnetohydrodynamics) does not explicitly present the relation of electric currents and electric fields in fully ionized plasma, and leads to some unexpected concepts, such as ``the magnetic frozen-in plasma'', magnetic reconnection etc. In the single fluid model, the action between electric current and magnetic field is not considered. In the two-fluid model, the derivation is based on the two dynamic equations of ions and electrons. The electric current in traditional generalized Ohm's law depends on the velocities of the plasma, which should be decided by the two dynamic equations. However, the plasma velocity, eventually not free, is inappropriately considered as free parameter in the traditional generalized Ohm's law. In the present paper, we solve the balance equation that can give exact solution of the velocities of electrons and ions, and then derive the electric current in fully ionized plasma. In the case ignoring boundary condition, there is no electric current in the plane perpendicular to the magnetic field when external forces are ignored. The electric field in the plane perpendicular to magnetic field do not contribute to the electric currents, so do the induced electric field from the motion of the plasma across magnetic field. The lack of induced electric current will keep magnetic field in space unaffected. The velocity of the bulk velocity of the plasma perpendicular to magnetic field is not free, it is decided by electromagnetic field and the external forces. We conclude that the bulk velocity of the fully ionized plasma is not coupled with the magnetic field. The motion of the plasma do not change the magnetic field in space, but the plasma will be confined by magnetic field. Due to the confinement of magnetic field, the plasma kinetic
energy will be transformed into plasma thermal energy by the Lamor motion and collisions between the same species of particles inside plasma. Because the electric field perpendicular to magnetic field do not contribute electric current, the variation of magnetic field will transfer energy directly into the plasma thermal energy by induced electric field. The heating of plasma could be from the kinetic energy and the variation of magnetic field.