Lorentz force sigmometry: a novel technique for measuring the electrical conductivity of solid and liquid metals

In this paper, a novel method to measure the electrical conductivity of solid and molten metals is described. We term the method 'Lorentz force sigmometry', where the term 'sigmometry' refers to the letter sigma σ, often used to denote the electrical conductivity. The Lorentz force sigmometry method is based on the phenomenon of eddy currents generation in a moving conductor exposed to a magnetic field. Based on Ampere's law, the eddy currents in turn generate a secondary magnetic field; as a result, the Lorentz force acts to brake the conductor. Owing to Newton's third law, a measurable force, which is equal to the Lorentz force and is directly proportional to the electrical conductivity of the conductive fluid or solid, acts on the magnet. We present the results of the measurements performed on solids along with the initial measurements on fluids with a eutectic alloy composition of Ga⁶⁷In^20.5Sn^12.5; detailed measurements on molten metals are still in progress and will be published in the future. We conducted a series of experiments and measured the properties of known electrical conductive metals, including aluminum and copper, to compute the calibration factor of the device, and then used the same calibration factor to estimate the unknown electrical conductivity of a brass bar. The predicted electrical conductivity of the brass bar was compared with the conductivity measured with a commercial device called 'SigmaTest'; the observed error was less than 0.5%. (paper)