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We derive exact analytical expressions for the quasi-stationary field quantities due to circular turns carrying current in the presence of conducting prolate and oblate spheroids. We use these expressions to generate numerical results of specified accuracy for the field quantities inside and outside the spheroids, as well as for the Joule losses inside them and the forces acting upon them. We present selected results in a normalized form for determined, extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis, and the position of the inducing turns relative to the spheroids. The results constitute reference data for comprehensive comparisons of results from approximate volume methods or from boundary impedance models used for real-world conductors in the presence of nonuniform external magnetic fields.