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Analytical solutions are given for the eddy currents (magnitude and phase) induced in a cylindrical shell of infinite length and thickness by a 3-phase winding of finite length placed coaxially inside the shell. The flux densities and associated loss are also determined. Solutions are obtained in integral form by solving Maxwell's equations and applying appropriate boundary conditions. Use is made of the magnetic vector potential. The loss is calculated by applying Poynting's theorem on the internal surface of the shell. Numerical results are obtained on a digital computer for different radii of the shell by using the Gauss- Laguerre method. The limitations of the method are discussed. The conducting material is nonmagnetic and the solutions are valid for all frequencies smaller than those of the optical spectrum. Tests were made on an aluminium shell and measurements of field values in the air were compared with the corresponding theoretical results.