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A general technique is described for combining a finite element representation of a quasi-stationary nonlinear magnetic field problem and the loop equations for all circuits, moving or stationary, which interact with the field. Various power quantities associated with the field and with each independent circuit loop can be estimated directly. Methods are presented for time integration of the first-order matrix differential equation describing both field and circuits. Saturating nonlinearities are treated iteratively. In particular, a transient problem in an idealized induction motor is solved. When permitted to reach steady state this solution yields points on the torque versus slip curve for the motor.