Current displacement of a solid cylindrical conductor placed in a semiclosed slot, taking into account the leakage field in the gap

The field problem is solved assuming a constant magnetic field strength in the middle of the slot opening. Adapting the vector potential in gap and conductor, which has been expanded into Fourier series and described in different coordinate systems, one obtains a system of linear complex equations for the Fourier coefficients. The calculation of surface current density and surface field strength is checked by measuring the bar current and comparing it with a value deduced from the measurement of the voltage drop at the surface of the bar. This comparison becomes significant due to the fact that these quantities converge badly and determine the bar impedance by means of Poyntings's vector. Finally a comparison is made with the normal approach, which has high practical importance, and which takes the magnetic field strength on the surface of the conductor as a given boundary condition. This comparison shows the advantages of the analysis presented over the conventional approximation. At last a finite element (FE) solution for this problem is given.