Duality of the electric covering fieldmill and the fluxgate magnetometer

This work treats two dc field sensors. The first sensor is the "covering fieldmill" that is employed to measure dc electric fields. The second sensor is the "fluxgate magnetometer" that is utilized to measure dc magnetic fields. An unusual approach is suggested to deal with the devices evaluation. It is shown that both devices can be associated with related ac field sensors-electric and magnetic. This association leads to modeling the dc sensors by Thevenin circuit models. It is then shown that in both cases the coupling between the sensors output circuitry and the measured field sources is due to series time-varied reactances. This enables a similar analytical treatment to both devices. Furthermore, it is also suggested that both sensors are related to the large family of antennas. As a result, an unusual way is found to relate the sensors output signal to the measured field. It is well known that the signal in electric antennas is related to the measured field times the effective antenna length. It is therefore relatively easily acceptable that also in the dc electric sensor case a similar relationship holds. The work, however, suggests that this relationship (that non relates the output signal to the measured dc magnetic field times the effective magnetic structure length) also holds in the fluxgate magnetometer case. An extension of this result is useful when attempting to measure nonuniform dc magnetic fields and is treated toward the end of the paper.