The watt-balance operation: magnetic force and induced electric potential on a conductor in a magnetic field

TL;DR

This paper revisits the fundamental equations in watt balance experiments, analyzing microscopic effects and confirming that non-uniform electron density corrections do not impact the measurement of the Planck constant.

Contribution

It provides a microscopic analysis of magnetic force and induced potential in watt balances, showing that electron density variations are negligible for the experiment's accuracy.

Findings

Microscopic equations align with macroscopic models.

Electron density non-uniformities are insignificant.

Watt balance measurements remain unaffected by these corrections.

Abstract

In a watt balance experiment, separate measurements of magnetic force and induced electric potential in a conductor in a magnetic field allow for a virtual comparison between mechanical and electrical powers, which leads to and an accurate measurement of the Planck constant. In this paper, the macroscopic equations for the magnetic force and the induced electric potential are re-examined from a microscopic point of view and the corrective terms due to a non-uniform density of the conduction electrons induced by their interaction with the magnetic field are investigated. The results indicate that these corrections are irrelevant to the watt balance operation.