DETERMINATION OF QUASI-STATIONARY ELECTROMAGNETIC FIELDS IN FERROMAGNETIC CONDUCTORS BY VARIATIONAL METHOD

Abstract

The paper gives a method for the determination of the quasi-stationary electromagnetic fields brought about by a harmonically varying current flowing in a ferromagnetic conductor of arbitrary cross section. Nonlinearity is neglected and a two-dimensional model is employed. The quasi-stationary field in the conductor is obtained by the solution of the differential equation for the vector potential at homogeneous Dirichlet boundary condition. The method presented yields a solution satisfying the differential equation approximately and the boundary conditions on the analytical or analytically approximated bounding curve exactly. The determination of the function satisfying the differential equation is reduced by variational calculus to finding the extremal function of a complex functional. Applying Ritz's procedure, the potential function is approximated by a function series. The approximating functions are constructed with the aid of R-functions to ensure that they satisfy the boundary conditions exactly. The method is illustrated by an example.