Uncertainty analysis of the BIPM susceptometer

Abstract

A magnetic susceptometer developed at the Bureau International des Poids et Mesures (BIPM) is used by many national laboratories to determine the magnetic properties of stainless-steel mass standards. This device relies on a small, cylindrical magnet to simulate a magnetic point dipole. According to simple theoretical considerations, (a) the uncertainty in the magnetic moment contributes weakly to the combined uncertainty of any measured susceptibility provided that unknowns are measured relative to a standard of similar size; (b) a cylindrical magnet with a height-to-diameter ratio of 0.87 best approximates a point dipole; and (c) the magnetic moment of the cylindrical magnet used can be determined by the susceptometer itself. Experimental tests of these assertions are presented. The properties of the cylindrical magnet generally become more important when determining the susceptibility of "small"-sized samples relative to a "large" standard. Small samples provide additional challenges, which are discussed in the context of a more general uncertainty analysis.

Improved methods for determining the susceptibility of weights

“…The weights' and reference standard's dimensions were measured by a Vernier calliper traceable to MIRS. For the NdFeB magnet constant permanent magnetization can be assumed as a reasonable approximation [4].…”

“…Possible magnetic remanence of the sample is not taken into account. With known value of the magnitude m of the permanent magnet's magnetic moment m, and with the assumption that it behaves as a point dipole [1,3,4], where the magnetic field of the magnetic dipole moment can be found in [6], we are able to write the force on the sample F a :…”

“…A method is developed, which takes into account the actual dimensions of magnets, which can also help us make a better estimation of the measurement uncertainty of the magnetic dipole moment. The method gives additional information to a similar topic discussed in [4].…”

“…This paper discusses the theoretical and practical aspects of determination of the volume magnetic susceptibility of the OIML weights taking into account their actual shape. The theory of the BIPM susceptometer was adopted according to [1,3,4], and a similar susceptometer was constructed by MIRS. Then a physical model was developed, which took into account the actual shape of the weight, without approximation of the shape.…”

“…Similarly, the literature [1,4] describes a method for determining the magnetic point dipole moment using a susceptometer. It has been proved that a simple method could be used to find the magnitude of the magnetic moment, provided that three geometrically similar magnets are available.…”