*2.1. Field Probes Functional Principle*

The field probes used for measurements belong to a group of transmitters for which the signal (output voltage) is proportional to the rate of change of the measured quantity, i.e., to the derivative of the measured quantity. This applies both to the electric field probe, based on a capacitive transducer, and to the magnetic field probe using an inductive transducer.

The B-dot and D-dot probes are available in two versions: single ground type for fast alternating fields at the surface, and differential free field type for fast alternating fields in space. For the B-dot ground magnetic field probe, the output signal can be written with Equation (1). The output signal for the D-dot ground probe is given by Equation (2).

$$\mathbf{U}(\mathbf{t}) = \mathbf{A}\mathbf{e}\mathbf{q}\frac{\mathbf{d}\mathbf{B}(\mathbf{t})}{\mathbf{d}\mathbf{t}} = \mathbf{A}\mathbf{e}\mathbf{q}\cdot\mathbf{\mu}\_{\mathbf{o}} \cdot \frac{\mathbf{d}\mathbf{H}(\mathbf{t})}{\mathbf{d}\mathbf{t}}\tag{1}$$

$$\mathbf{U}(\mathbf{t}) = \mathbf{R} \mathbf{s} \cdot \mathbf{A} \mathbf{e} \mathbf{q} \frac{\mathbf{d} \mathbf{D}(\mathbf{t})}{\mathbf{d}\mathbf{t}} = \mathbf{R} \mathbf{s} \cdot \mathbf{A} \mathbf{e} \mathbf{q} \cdot \mathbf{e}\_o \cdot \frac{\mathbf{d} \mathbf{E}(\mathbf{t})}{\mathbf{d}\mathbf{t}},\tag{2}$$

where: Aeq is the equivalent area of the single sensor; B is the magnetic flux induction, H is the magnetic field strength; μ<sup>o</sup> is the vacuum permeability. Rs is the impedance seen by a single channel of the sensor, D is electrical induction, E is electrical field strength; ε<sup>o</sup> is vacuum permittivity.

As can be seen from Equations (1) and (2), the output signal is proportional to the physical dimensions of the probe, but most importantly it is proportional to the rate of change of the field—the derivative of the field. This forces the necessity of signal integration to obtain the value of measured field.
