  The traditional generalized Ohm's law in MHD do not explicitly present the
relation of electric currents and electric fields in fully ionized plasma, and
lead to some unexpected concepts, such as "the magnetic frozen-in plasma",
magnetic reconnection etc. In the present paper, we solve the balance equation
can give exact solution of the velocities of electrons and ions, and then
derived 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.
