Magnetic shielding of 3-phase current by a composite material at low frequencies

Abstract

Electromagnetic shielding at microwave frequencies (MHz and GHz) can be accomplished by attenuating the waves using ferromagnetic resonance and eddy currents in conductive materials. This method is not as effective at shielding the quasi-static magnetic fields produced by low-frequency (kHz) currents. We explore theoretically the use of composite materials - magnetic nanoparticles embedded in a polymer matrix - as a shielding material surrounding a 3-phase current source. We develop several methods to estimate the permeability of a single magnetic nanoparticle at low frequencies, several hundred kHz, and find that the relative permeability can be as high as 5,000-20,000. We then use two analytic effective medium theories to find the effective permeability of a collection of nanoparticles as a function of the volume filling fraction. The analytic calculations provide upper and lower bounds on the composite permeability, and we use a numerical solution to calculate the effective permeability for specific cases. The field-pattern for the 3-phase current is calculated using a magnetic scalar potential for each of the three wires surrounded by a cylinder with the effective permeability found above. For a cylinder with an inner radius of 1 cm and an outer radius of 1.5 cm and an effective permeability of 50, one finds a reduction factor of about 8 in the field strength outside the cylinder.