The principles of the complete measurement of an off-centred elementary magnet on a spinner magnetometer with a coil sensor

The aim of the present treatise is to show that, albeit a precise measurement of a magnetically inhomogeneous sample may not be obtained on a traditional spinner magnetometer, it is still possible to get one on a modified spinner provided that magnetic inhomogeneity can be correctly modelled by an elementary magnet of moment m which is offset (l) relative to the geometrical centre of the sample. Following the deduction of the equations of the response of the pick-up coils to such a magnet rotated within the coils (forward problem), a proposal is presented as to how to modify the pick-up unit in order to make the magnetometer adaptable to the complete measurement of both magnetic moment (m) and eccentricity (l) (inverse problem). The proposed modification, pick-up coils that can be set both vertically as well as about the vertical axis, makes it theoretically possible first to measure |l|, then to eliminate the effect of it from the response of the pick-up coils leaving a record from which m can be extracted unequivocally. In practical realisation, the measurements will have to be carried out with the pick-up unit tuned in resonance with the frequency of the sample rotation, and optionally with the treble of it if it is deemed necessary for checking or improving upon the precision of measurement.