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Solutions for electromagnetic field problems are usually found by methods derived from either finite difference techniques or finite element approaches. This paper discusses the application of the method of magnetic charges to the solution of three-dimensional problems where high permeability materials are present. Remarkable savings in computer time are possible by using the magnetic charge concept in conjunction with other techniques. The method has been applied to the case of an iron cube placed in the field of a solenoid. Comparable analytic and experimental results are obtained. The method is very rapid, yielding inexpensive solutions to difficult geometries. Hence its advantages far outweigh its disadvantages. The work presented in this paper is a preliminary study intended for future application in the calculation of the electromagnetic fields of power transformers.