The magnetic-field distribution is analysed for the case of an aluminium plate excited by a circular current loop, and an expression for the eddy-current loss in the plate is deduced. This analysis is tested by comparison with measurements on a model which closely resembles the theoretical geometry, and the results are shown to be in close agreement. A method for measuring the eddy-current losses in plates is described. It is found that the losses in thin plates can be abnormally high. It is shown that the image theory may be used with nonmagnetic conducting plates for all plate thicknesses greater than 0.8 times the characteristic depth of flux penetration in the material. The magnetic field of large air-cored reactors is analysed, and expressions are obtained for the inductance and the loss in the flux shields. It is believed that this method is capable of giving more accurate results than have been hitherto obtained.