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This paper develops, for the first time, a 3-dimensional theory of the eddy-current coupling. It compares, again for the first time, experimental results obtained on various couplings with the theoretical computations and shows a very close agreement between the two. The curves give slip-torque characteristics of eddy current couplings at various excitations with poles ranging from 12 to 42. The paper is highly mathematical and offers a unique example of the application of Maxwell's electromagnetic field equations to a practical engineering problem.