In order to solve the problem that the relative permeability of the permalloy is missing and difficult to measure accurately in an extremely weak magnetic field (EWMF, <1 nT), a method to measure the permeability in EWMF based on the Rayleigh model is proposed in this paper. In this method, the Rayleigh model for the magnetic material was first introduced. Then, the test system for measuring the permeability of permalloy for the standard ring specimen was set up. Based on the test data and the Rayleigh model, the functional expression applied to obtain the permeability in EWMF is achieved. Finally, the feasibility and accuracy of the method are verified by the permeability measurement of the custom large-size ring specimen in EWMF (<1 nT) and residual field measurement based on the four-layer shielding cylinder. This method can obtain the relative permeability in any EWMF and avoid test errors caused by extremely weak magnetization signals.
Keywords: Rayleigh model; extremely weak magnetic field; permalloy; relative permeability.