A Low-Cost and Accurate Method for Measuring Weak Magnetic Susceptibilities

The magnetic properties of any substance in nature can be condensed into a unique parameter: the volume magnetic susceptibility
$\chi $
. Its value and sign indicate if a given material is diamagnetic, paramagnetic, or ferromagnetic. Accurate measurements of
$\chi $
for paramagnetic or diamagnetic substances are generally performed with high-tech devices with relatively complex methods. Simple methods proposed to determine
$\chi $
for everyday materials result in inaccurate measurements (
$\ge 50$
%). Here, we propose a simple, practical, and low-cost method to accurately obtain
$\chi $
, via measurements performed with an ordinary balance and a set of neodymium magnets. The force exerted by the magnets on a given sample is sensed by the balance and, via comparison with exact numerical calculations of the magnetic force on the whole sample, the magnetic susceptibility can be determined. The shape, size, and position of the sample relative to the magnets as well as the number of neodymium magnets are optimized to maximize the magnetic force on the sample and, therefore, minimize the experimental uncertainties in the determination of
$\chi $
.