Towards analytical calculation of the magnetic flux measured by magnetometers

This paper reviews magnetic flux signal calculations through pick-up loops using vector spherical harmonic expansion under the quasi-static approximation, and presents a near-analytical method of evaluating arbitrary parametrizable for each degree. is done by simplifying surface integral (2D) into line (1D). For special case tangential circular sensors, we present fully analytical recursion calculation. We then compare commonly-used cubature approximations to our (near-)analytical forms, show that suffer from increasing errors higher spatial frequency components. suggests need more accurate evaluations increasingly sensitive sensors are being developed, forms themselves solution this problem.