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

(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

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

where is the permeability of free space, which will be self sustaining if
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Note that you have to supply energy to counter the opposing torque on the disk required to cut the field lines (Lenz's law).Also, the system requires differential rotation. It must also have the correct topology (if the orientation of the wire loop is reverse, the dynamo will not function). Also, because the equation is linear, either sign of magnetic field works equally well. The process is described by the dynamo equation.The mechanism for generating the Earth's magnetic field is believed to be a dynamo and is called the geodynamo.