DETERMINATION OF THE MAGNETIC FIELD ENERGY OF A TOROIDAL COIL WITH A FERROMAGNETIC CORE

Abstract

The article demonstrates a method for taking into account the nonlinear dependence of the relative magnetic permeability of a ferromagnet on the magnetic field strength when determining the field energy and inductance of a coil on a toroidal core. Unlike the simplified physical model of the coil, where the authors use the average value of the relative magnetic permeability 〈μ〉, it is shown that the calculation result is determined by the function ( ) , H H μ and is more correct than by the average value of the relative magnetic permeability. In the examples for calculating the coil parameters, reference dependences of the magnetic field induction on its strength for the ARMCO ferromagnetic material are used. The differences in the results obtained for the field energy and inductance of the coil according to our method and according to the classical method using the average value of the relative magnetic permeability significantly depend on the boundaries between the maximum and minimum values of the magnetic field strength in the core. It was found that the differences in the determination of the magnetic field energy in the core of the coil according to the proposed method and in comparison with the results according to the simplified method, where the magnetic permeability is considered unchanged, can reach 30 %., At the same time, the sign of such differences also depends on the current strength, or on the limits of change in the magnetic field strength in the cross-sectional area of the core. The differences in both the field energy values and the coil inductance increase to 34 % with an increase in the ratio of the outer and inner radii of the core, compared with the results where the magnetic permeability is considered unchanged. The use of software when determining the area of figures under function graphs helps to simplify individual calculations and increase the accuracy of the results obtained. The direction of using the method of determining the energy and inductance of a coil in computational and graphical work has been determined, for which the student will be able to use the magnetization curve obtained during laboratory work.