The response of longitudinal and transverse pickup coils to a misaligned magnetic dipole

The responses of magnetic pickup coils to various orientations and positions of a point dipole are considered. General solutions which describe the response functions are derived and analyses of the results are presented. The apparent magnetic moment, as determined from these functions, contain significant errors when the dipole is misaligned radially or directionally. The errors fall into three categories: radial off-centering of a correctly oriented dipole, angular misalignment of a centered dipole, and angular misalignment of a radially off-centered dipole. One simple experimental test with a commercial magnetometer showed a 34% error in the apparent moment due to radial off-centering. Practical error correction and minimization involve sample centering and rotational orientation about ẑ for transverse measurements, and include an additional adjustable parameter in the fitting function. Modest attention to these factors will reduce errors from ≊100% difference to ≤1%. The general nature of the calculations indicate that such effects exist for any type of inductive magnetometer.