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A mathematical model using an integral-equation/singularity-method approach is derived for determining the magnetic field and electromagnetic forces induced by current-carrying conductors in a region bounded by 3-D material-body surfaces which have complex configurations. Special analytical and numerical techniques that eliminate near-field computational difficulties and bypass the cumbersome matrix manipulations required by other integral-equation approaches are described. A comprehensive computer program package has been developed using this approach for obtaining the 3-D solutions in the end region of a turbine-generator due to armature end windings. Special computational techniques for handling the complex end-winding and surface geometry are described and detailed numerical results are presented for the 3-D field solution and the forces acting on the conductors.