We propose a systematic method for interfacing different 2-D low-frequency electromagnetic field slices and nonidentical multi-port circuit networks using finite-element (FE) and modified nodal analyses. Each independent field slice has its own length, geometry, materials, boundary conditions, and number of filamentary and massive conductors. Similarly, each multi-port circuit network can have different circuit elements, topology, and number of ports. As a result, field slices are not required to be successively connected, since multi-port circuit networks can exist between them. Thus, solutions for virtually any possible configuration of 2-D circuit-field coupled systems are possible. The number of slices and multi-port networks does not affect the general form of the final system of equations, which is symmetric for most practical cases. Although we developed the methodology for 2-D time-harmonic magnetic problems, it can be readily extended to the transient case. We analyzed an induction motor to test the proposed multi-slice FE approach and validated the results using the total short-circuit leakage reactance and commercial software (Flux2D).