In the presence of a vertical magnetic field, the rotating disk generates an electromotive force which drives a current. The current generates a field which amplifies the existing field. The seed field can then be turned off and the system will be self-sustaining. This process is called a (disk) dynamo. Let be the seed voltage, then

(1)

(in MKS) where v is the speed of the disk, B is the magnetic field, and r is the radius of the disk. The current is then

(2)

where R is the resistance of the disk. This current creates a magnetic field

(3)

where is the permeability of free space, which will be self sustaining if

(4)

Alpha Effect, Dynamo Equation, Frozen Flux Approximation, Omega Effect