Here, we derive the basic equations of magnetohydrodynamics.
Differences from hydrodynamics are the Lorentz force in the equation of motion and the induction equation
of magnetic field.
The Lorentz force is written as

(B.1) |

(B.2) |

The Faraday's law
and the Ohm's law
( is the electric conductivity)
lead the induction equation of the magnetic field as