Models for the nearfield interaction of a magnetic field from point sources representing transformers and power supplies and a ferromagnetic cylindrical shell

Abstract

This paper describes models of the magnetic field interactions from various sources and a physical blockage. The sources represent power supplies, transformers, and cables; the physical blockage is a cylindrical shell. The sources are modeled as vector fields in the magnetostatic limit. Boundary conditions applied at the outer and inner interfaces of the cylindrical shell require that the normal component of the B field and the tangential component of the H field be continuous at the outer and inner interfaces. The source fields are transformed to the coordinate system of the cylindrical shell, where the final solutions are given. The source fields are expanded in binomial expansions, and the response fields outside, within, and in the interior region of the cylindrical shell are expanded in Legendre polynomial expansions. Upon application of the boundary conditions, a system of linear equations is generated by matching powers of sine and cosine functions in the binomial and Legendre polynomial expansions. The solutions of this system of equations yield the coefficients of expansion of the Legendre polynomials. The number of equations generated depends on the extent of the expansions, which, in turn, depends on the accuracy that is required. After solving for the coefficients of expansion, the coefficients are substituted back into the Legendre polynomial field equations, and the gradients are taken to obtain the vector fields. These fields are then added to the source fields to obtain the final solutions.