Correlation of the air-gap vector potential of an induction motor with the magnetising current

As a preliminary to any attempt to unify the field and circuit theories of rotating electric machinery, it is necessary, if possible, to develop a one-to-one relationship between a field quantity and a circuit quantity. In the paper, Maxwell´s equations are applied to the slip-ring induction motor using homogenised permeabilities in the stator and rotor slotted regions. The mathematically exact solution is checked by reference to a conventional design. A simple and approximate solution is derived, and is found to be essentially the same as the normal design treatment. The air-gap vector potentialA is shown to be related to the current i which produces it, by the simple formula A=6/¿3 T/¿LS i sin ¿¿ where T is the number of turns per phase, ¿ the number of pole pairs, L the axial length, and S, for which an expression is given, the reluctance per pole-pitch.