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This paper presents a closed-form solution of Maxwell's equations in squirrel-cage induction motors. The solution is obtained for a cylindrical multilayer geometry. The squirrel cage is represented by an equivalent anisotropic homogeneous medium. The effect of stator slots and teeth is included by a second anisotropic homogeneous medium. The induction motor is modeled as six concentric cylindrical layers representing the different construction components of the motor. The governing partial differential equations are solved for the excitation source, conducting, and nonconducting regions. The obtained formulas allow for efficient calculations of machine performance which may help the motor designer to select the proper parameters of the machine that fit the design requirements. Accuracy of the method is verified against finite element simulations, a commercial motor design program, and experimental results.