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The traditional generalized Ohm's law in MHD do not explicitly present therelation of electric currents and electric fields in fully ionized plasma, andlead to some unexpected concepts, such as "the magnetic frozen-in plasma",magnetic reconnection etc. In the present paper, we solve the balance equationcan give exact solution of the velocities of electrons and ions, and thenderived the electric current in fully ionized plasma. In the case ignoringboundary condition, there is no electric current in the plane perpendicular tothe magnetic field when external forces are ignored. The electric field in theplane perpendicular to magnetic field do not contribute to the electriccurrents, so do the induced electric field from the motion of the plasma acrossmagnetic field. The lack of induced electric current will keep magnetic fieldin space unaffected. The velocity of the bulk velocity of the plasmaperpendicular to magnetic field is not free, it is decided by electromagneticfield and the external forces. We conclude that the bulk velocity of the fullyionized plasma is not coupled with the magnetic field. The motion of the plasmado not change the magnetic field in space, but the plasma will be confined bymagnetic field.  Due to the confinement of magnetic field, the plasma kinetic energy will betransformed into plasma thermal energy by the Lamor motion and collisionsbetween the same species of particles inside plasma. Because the electric fieldperpendicular to magnetic field do not contribute electric current, thevariation of magnetic field will transfer energy directly into the plasmathermal energy by induced electric field. The heating of plasma could be fromthe kinetic energy and the variation of magnetic field.

A Theory about Electric Current and Heating in Plasma