The influence of time varying magnetic fields on the determinations of Newton's constant at the Bureau International des Poids et Mesures

The values of Newton's constant of gravitation, G, reported by determinations at the International Bureau of Weights and Measures (BIPM) in Quinn et al (2001 Phys. Rev. Lett. 87 111101/1-111101/4) and in Quinn et al (2013 Phil. Trans. R. Soc. A 372 2-28) are some 200 parts per million (ppm) larger than the value of 6.67430 x 10-11 m3 kg-1 s-2 which was recommended by CODATA in Tiesinga et al (2018 J. Phys. Chem. Ref. Data 50 033105). The CODATA value has an assigned uncertainty of 22 ppm and the reported uncertainties in the BIPM values were 41 ppm and 25 ppm, respectively. The discrepancy therefore amounts to about seven times the combined uncertainty of the latest BIPM and CODATA values. We examine experimentally the hypothesis that the difference is due to a bias produced by stray alternating (AC) magnetic fields in the vicinity of the experiment. Whilst the BIPM torsion balance was located at the University of Birmingham a coil, having a similar scale to the balance, was used to generate AC magnetic fields of magnitude approximately 1 mu T which in turn produced torques of magnitude approximately 0.2 % of the gravity torque. The magnitudes of these torques were compared with simple analytical models and finite element analyses. Measurements in the laboratory in Birmingham and, more recently, at BIPM give a very conservative upper limit on the rms magnitude of ambient AC magnetic fields of 100 nT. As the torque was demonstrated to vary with the square of the ambient field, these observations and our analyses suggest an upper limit to the possible bias in the BIPM determinations of the order of 20 ppm. It is therefore unlikely that torques due to ambient magnetic fields could have significantly biased values of G determined at BIPM.