Magnetohydrodynamics (or "MHD") is the study of the motion of an electrically conducting fluid in the presence of a magnetic field.

The system is non-trivial since the magnetic field affects the motion of the fluid, which in turn affects the strength of the magnetic field
(for example the motion of the earth's liquid core maintains our terrestrial magnetic field).

The basic equations of MHD are really a sub-set of Maxwell's equations.

We take the 4 given Maxwell equations and reduce them into a single equation for the magnetic field, B.
The resulting equation is called the Magnetic Induction Equation. Click here to see how we arrive at it.