rotating worlds with rotating magnetic field...

The rotating magnetic field is a fundamental principle in physics and one of the greatest discoveries of all times.  In February 1882, Tesla was walking with a friend through a city park in Budapest, Hungary reciting stanzas from Goethe's Faust.  The sun was just setting.  Suddenly the solution of the rotating magnetic field, he had been seeking for a long time, flashed through his mind.  At this very moment he saw clearly in his mind an iron rotor spinning rapidly in an rotating magnetic field produced by the interaction of two alternating currents out of step with each other.  One of the ten greatest discoveries of all times was born at this glorious moment.

Goethe's Faust was an inspiration for Nikola Tesla.  He knew by heart the Faust.  By reciting the Faust in the park in Budapest, he discovered the rotating magnetic field which is the heart of his induction motor and alternating current electricity.  It is also a basis for MRI technology, therefore Tesla's name was honored with the Tesla Unit, used to measure the capacity of MRI machines.

In this painting of 1829-31Goethe is shown dictating to his secretary the second part of the Faust.  The small and simply furnished study room, which he called 'humble quarters', suited his inner creative life.  By the time of this portrait Goethe was already a world figure, a man of unique character and abilities who had a widespread influence on his own times.

A symmetric rotating magnetic field can be produced with as few as two polar wound coils driven at 90 degrees phasing. However, 3 sets of coils are nearly always used because it is compatible with symmetric 3 phase ac suppl. The three coils are driven with each set driven 120 degrees in phase from the others. For the purpose of this example, the magnetic field is taken to be the linear function of the coil's current.

Sine wave current in each of the coils produces sine varying magnetic field on the rotation axis. Magnetic fields add as vectors.

Vector sum of the magnetic field vectors of the stator coils produces a single rotating vector of resulting rotating magnetic field.

The result of adding three 120-degrees phased sine waves on the axis of the motor is a single rotating vector. The rotor has a constant magnetic field. The N pole of the rotor will move toward the S pole of the magnetic field of the stator, and vice versa. This magneto-mechanical attraction creates a force which will drive the rotor to follow the rotating magnetic field in a synchronous manner.

U.S. Patent 381968: Mode and plan of operating electric motors by progressive shifting; Field Magnet; Armature; Electrical conversion; Economical; Transmission of energy; Simple construction; Easier construction; Rotating magnetic field principles.

A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect was utilized in early alternating current electric motors. A rotating magnetic field can be constructed using two orthogonal coils with a 90 degree phase difference in their AC currents. However, in practice such a system would be supplied through a three-wire arrangement with unequal currents. This inequality would cause serious problems in the standardization of the conductor size. In order to overcome this, three-phase systems are used where the three currents are equal in magnitude and have a 120 degree phase difference. Three similar coils having mutual geometrical angles of 120 degrees will create the rotating magnetic field in this case. The ability of the three phase system to create the rotating field utilized in electric motors is one of the main reasons why three phase systems dominate in the world electric power supply systems.
Rotating magnetic fields are also used in induction motors. Because magnets degrade with time, induction motors use short-circuited rotors (instead of a magnet) which follow the rotating magnetic field of a multicoiled stator. In these motors, the short circuited turns of the rotor develop eddy currents in the rotating field of the stator which in turn move the rotor by Lorentz force. These types of motors are not usually synchronous, but instead necessarily involve a degree of 'slip' in order that the current may be produced due to the relative movement of the field and the rotor.