Mutual inductance and magnetic force calculations between thick bitter circular coil of rectangular cross section with inverse radial current and filamentary circular coil with constant azimuthal current

Abstract

In many engineering applications, the coils of different geometrical shapes are used. Usually, these coils (circular, right etc.) are with the constant currents in different directions. In the literature, there are many papers on the calculations of the magnetic fields of the circular coils with the constant azimuthal currents or the calculations of the mutual inductance and the magnetic force between them. In some applications, where the high intensity magnetic fields are required the circular metal plates and insulating spacers are used with the inverse radial current. Such configurations form an electromagnet named after its inventor Bitter. In this study, the authors calculate the mutual inductance and the magnetic force between the thick Bitter coil of rectangular cross-section with the inverse radial current and the circular filamentary coil with the constant azimuthal current. The semi-analytical and the analytical expressions of these quantities are obtained over complete elliptic integrals of the first and second kind as well as Heuman's lambda function. There is one simple integral which has to be solved numerically. The results of this method are compared by those obtained by the modified filament method for the presented configuration. All results are in an excellent agreement.