Vector potential due to a circular loop in a toroidal cavity in a high-permeability core

We present a Green's function for a circular loop in a toroidal cavity in a high-permeability material. We show that under certain conditions, Green's function may be expressed in terms of Jacobi's theta functions. We demonstrate an application of such a Green's function in analyzing the performance of pot core transformers. Results compare well with the values obtained by other analytical methods and by the measurement.