Consider an electrically conducting fluid (i.e., a plasma). Ampère's law, ignoring the Maxwell displacement current term, states

(1)

where B is the magnetic field, is the permeability of free space, and J is the current density. Ohm's law, including the induction electric field, is

(2)

where is the electrical conductivity, E is the electric field, and v is the fluid velocity. Finally, Faraday's law states that

(3)

Cowling's Theorem, Dynamo, Frozen Flux Approximation, Hydromagnetic Equation, Magnetic Reynolds Number