Two simple models for analytical calculation of eddy currents in thin conducting plates

Two simple models are proposed for the analytical calculation of eddy currents induced by a time-varying magnetic field in thin conducting plates of various shapes. In the first model, it is assumed that the current paths are determined exclusively by the shape of the plate. This assumption makes evident a shape factor that characterizes the shape of the plate under investigation and is independent of the dimensions of the plate. Thus, several important parameters, such as the equivalent resistance of the plate, the total circulating current, etc., are expressed analytically as a function of this shape factor. The application of the model makes possible the estimation of the total eddy current, circulating in plates of any shape, but the accuracy of this estimate is strongly affected by the shape of the plate. This model is then improved for plates having symmetrical shapes by taking into consideration the principle of minimum energy dissipation. The results, obtained by the improved model for the total circulating current, are in good agreement with the results obtained numerically as well as with analytical results obtained by the use of variational methods