Interaction of Magnetic Fields and Ferromagnetic Shields

An analytic procedure is developed for the purpose of determining the effectiveness of ferromagnetic shields in shielding against magnetic fields. The basic approach is to separate the magnetization relation of a ferromagnetic material into regions in which each region is characterized by a constant permeability. Maxwell's equations are then solved in each time-varying geometric region (which correspond to the regions of the magnetization relation) and the solutions are matched at interfaces. This procedure permits solutions for nonlinear shielding problems to be readily obtained using linear techniques.