Magnetohydrodynamics (MHD) is the study of the interactions between magnetic fields and electrically conducting fluids. The body (Lorentz) force acts on the fluid when electric current () flows at an angle to the imposed magnetic field (). The resistive heating is measured in Joules.

For a particle:

(9–11)

where is the charge on the particle.

For a continuous fluid:

(9–12)

where:

(9–13)