Improvement of Formula and Uncertainty of the Reference Magnetic Field for AC Magnetometer Calibration

In this paper, an ac magnetic field standard system for ac magnetometer calibration is described. The target field strength and frequency range are 7.162 A/m (9
$\mu\hbox{T}$
) and 50–60 Hz, respectively. The system to generate a reference magnetic field is based on the Helmholtz coil formula. However, this well-known formula is precise only for dc magnetic fields. Therefore, we improve the formula for ac magnetic fields. The uncertainties of the reference magnetic field and magnetometer calibration are also improved. Validation is achieved by using two calibration systems based on different principles.