Resolution of the paradox of the diamagnetic force on the Kibble coil

Published

January 13, 2021

Author(s)

Stephan Schlamminger, Shisong Li, Rafael Marangoni, Darine El Haddad, Qing Wang, Wei Zhao

Abstract

Employing very simple electro-mechanical principles known from classical physics, the Kibble balance establishes a very precise and absolute link between quantum electrical standards and macroscopic mass or force measurements. The success of the Kibble balance, in both determining fundamental constants ($h$, $N_A $, $e$) and realizing a quasi-quantum mass in the 2019 newly revised International System of Units, relies on the robustness of the magnetic field equivalence in two measurement modes, which, however, in reality, can not be perfect. Recent advances in the understanding of the current effect discovered the paradox of the diamagnetic force effect challenging the Kibble principle at uncertainty levels that are almost two orders of magnitudes larger than the reported uncertainties. The diamagnetic force appears in weighing mode and is caused by the coil current changing the magnetic field and as a result produce an unaccounted force that is modulated with the weighing current. Here we show that this diamagnetic force exists, but the additional force does not change the equivalence between weighing and velocity measurements. For typical materials and geometries the total relative effect on the measurement is $10^-9}$.

Citation

Nature - Scientific Reports

Volume

11

Pub Type

Journals

Download Paper

https://www.nature.com/articles/s41598-020-80173-9

Local Download

Keywords

Kibble balance, diamagnetic force, kilogram. revised SI

Citation

Schlamminger, S. , Li, S. , Marangoni, R. , El, D. , Wang, Q. and Zhao, W. (2021), Resolution of the paradox of the diamagnetic force on the Kibble coil, Nature - Scientific Reports, [online], https://www.nature.com/articles/s41598-020-80173-9 (Accessed October 21, 2025)