The equation describing the evolution of the magnetic flux density B in an electrically conducting fluid, given by
where v is the fluid velocity and is the magnetic diffusivity. If is constant, then the equation can be written in the form
From this equation, it can be shown that fluid motions cannot generate an exact dipole field or any other field with rotational symmetry (Cowling's theorem).
Cowling's Theorem, Dynamo Equation, Magnetohydrodynamics
