The Magnetic Field of a Current Loop Encircling an Axisymmetric Iron Core

Abstract

The effect of an iron transformer core on the field of a current loop is examined for two models of the core: (1) An infinite straight rod of high permeability aligned along the axis of symmetry, for which asymptotic expressions for the effect of the core are obtained and compared with numerical results. (2) A rectangular toroidal iron casing surrounding the loop. The latter model is more realistic because a return path is provided for the flux. For this model, the effect of air gaps is considered, and rapidly convergent series are obtained and numerical results are given. The significance of these results for tokamak equilibrium is indicated.