## 5 Time Response to Slow Changes in the Electric Field  
The sensors' response to the electric field's time change allows us to determine their basic dynamic parameters, i.e., sensitivity to the displacement current [12; 21]. The change in electric flux over time equals the change in electric charge on the sensor, which is nothing more than the definition of displacement current. The presented simulations are intended to compare sensors for detecting displacement currents. Excitation was defined as a very slow-changing slope, as presented in Figure 13.  
Figure 12: Deviation of electric field vector for ring 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.  
Its value changed from \(U_{0}=0\) V to \(U_{1}=1000\) V in time \(t_{s}=1\) s. Because the time dependency simulation type has to be changed to transient, simulation time was set to \(t_{sim}=1.2\) s and time step as \(t_{step}=0.01\) s. This current is described as the current in the external circuit. A sensor placed near the ground represents a simpler RLC circuit, like in Figure 14, so time response is a significant factor in describing its functionality. Resistance \(R\) results in the sensor ground connection, capacitance \(C\) is the sensor ground result, and inductance \(L\) is determined by sensor construction and geometry. The observed quantity was current density flows by thin conductor between sensor and ground and next integrated by its cross-section surface area. Figure 15 shows the variation in the electric current flows by sensor grounding connected and integrated by its cross-section surface area.  
The sensor's response to this excitation is in the form of fluctuations on the slopes, associated with the transient state (can be approximated by the envelope) and a flat section (steady state). The simulated variation in the current depends on the electrical capacitance of the sensor and the electric charge induced on its surface and can represent the displacement current. As shown in the Figure 15 reaction, each sensor on slowly changing electric field strength has high-frequency oscillations. The oscillations result from the external circuit (RLC) parameters through which the electric current flows. They occur at the beginning and end of the excitation slope. The oscillations result from the parameters of the external circuit through which the electric current flows. The ring-type sensor's current value and transient response are the highest (Figure 15c). The higher current value in the steady state is for all sensors placed at the height of 1 m (green color). This effect exists due to the larger effective area of the sensor. The transient response of the sensor is independent of the height of the sensor. Assuming that the derivative of the electric field concerning time or the second derivative of the electric potential represents the density of the displacement current [17]. Figure 15c shows the highest value of this current in a steady state in the ring-type sensor.  
Figure 14: Simple electrical diagram describing idea time response simulations.  
Figure 13: Time variable excitation—1000 V/s rising slope.