Magnetohydrodynamics is the beast which emerges when you combine the equations (Navier-Stokes) governing the motion of fluids, and the equations (Maxwell) governing electric charges and magnetic fields. If a fluid is electrically conductive, then that means flows in this fluid are affected by electrical currents. And electrical currents create magnetic fields, and those fields can exert forces and induce more currents in the surrounding material. This gets *extremely* complicated, because all the particles in the fluid are affecting their neighbours in two different ways at once.
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