## 4 The Collective Surface of the Sensors  
The nature of the presented currents is volumetric and spatial. The current density vector describes them \(\overrightarrow{J}\) (it contains all current components). The relation between the total current \(I\) through a surface and the current density \(\overrightarrow{J}\) might be calculated on the geometry of the sensor:  
\[I=\int_{S}\overrightarrow{J}^{\circ}\hbar da \tag{7}\]  
In this dependence, there is a component normal to the surface. It is imperative. The knowledge of the collecting area allows us to calculate the surface current value and assess the measured area's practical size [19; 20]. The shape of the selected collecting area is shown in Figures 10-12. It has been calculated with the Matlab environment, which has imported results from Ansys. Next, vectors of electric field strength characterized by each calculation point were analyzed as percentage deviation to the vertical direction. If this deviation was more remarkable than the assumed 5% taken as a reference level, this point could influence the analyzed sensor. The results of vector decomposition for each analyzed sensor are shown in the following figures (Figures 10-12). They present a 2-dimensional cut in the XZ surface (the Y coordinate was equal to zero)--calculation points were distributed with \(a=10\) mm distance. Figure 10: Deviation of electric field vector for flat type sensor: (**a**) placed equal to ground level (\(A=0\) m), (**b**) placed above ground level (\(A=1\) m). Areas shown in red represent electric field lines that will reach the sensor surface, reducing the field component. These areas represent the directional characteristics of the sensor. In the bright areas above the sensor, the electric field lines arrive perpendicularly, i.e., without changing their components. In order to compare the parameters of the sensors, the term \"effective area of the antenna\" was used. The effective area is the horizontal cross sections above the antenna through which the electric field line ends on the sensors' surface [11; 17; 20]. The air-earth current density can be determined based on the collected current in the external circuit of the sensor and the effective area. The effective area is approximately equal to the geometric area of the sensor when placed on the ground. In this case, the accumulated current is small, in the order of pA, and the measurement is carried out at the GEC electrode, which can cause significant distortion [10]. Figure 10 shows configurations of electric field lines obtained for the flat sensor (Wilson Antenna) model. For a sensor placed at ground level, as in Figure 10a, most field lines extend perpendicularly to the sensor's surface. They are equal to the horizontal component--\(E_{z}\). When the flat sensor is located at a height of 1 m in the shaded areas, the component in the E field vector begins to dominate the \(E_{x}\) component. The effective area increases significantly, as seen in the vertical section of Figure 10b. At a height of 1 m, it is about 4.4 m. The sensor of the grater type has a similar size of the effective area (Figure 11) as the flat antenna. Vertical elements in the geometrical structure of the antenna do not have a significant impact on the shape of the effective area. Figure 12 shows the electric field of a ring-type sensor. The height of the ring, which is equal to 25 cm, causes the collecting surface in the vertical section to be about 2 m. Placing the sensor at a height of 1 m results in a collecting surface equal to almost 6 m. On this basis, it can be concluded that a sensor with only a vertical geometric configuration can  
Figure 11: Deviation of electric field vector for grater type sensor: (**a**) placed equal to ground level (\(A=0\) m), (**b**) placed above ground level (\(A=1\) m). Areas shown in red represent electric field lines that will reach the sensor surface, reducing the field component. These areas represent the directional characteristics of the sensor.