## 3 Results  
Analyses were performed using an electromagnetic field formulation based on accelerating charges instead of the traditional dipole approach. Thus, it was possible to obtain the final field expressions in a closed and compact form. The load-dependent component \"(e)\" was examined under the heading of the Rusck closed formulation and the coupling model, starting with a positive value, \(\mathrm{e}_{\Phi}^{0}\). In Figure 10, the distance to the point where the LEMP falls according to different current values is determined as 100 m from the transmission line. The reason for choosing this value is to ensure that the pulse is close to the power transmission lines. The vertical electric field value formed at the foundation of the overhead line at this distance is shown in Figure 11. This value drops to zero when the return pulse approaches the cloud. The \(\mathrm{e}_{\mathrm{A}}\) component due to the LEMP current starts to increase from zero. Initial values are obtained if the t = r/c equation is written instead of t in the equations in Equations (21) and (22). In Figures 11 and 12, \(\mathrm{e}_{\Phi}-\mathrm{e}_{\Phi}^{0}\), \(\mathrm{e}_{\mathrm{A}}\) and \(\mathrm{b}_{\Phi}\) are analyzed and represented analytically. Figure 10: The vertical electric field and scalar component for different LEMP currents for r = 100 m and z = 0 depending on the load distribution throughout the LEMP channel (solution for the function in Equations (21) and (22)). In Figure 11, the vector components of the electric field formed at the base of the overhead line located 100 m away from the point where the LEMP fell are shown for different current values. In Figure 12, the magnetic field values for the same configuration are denoted. If the equation \"\(\beta\cdot\frac{\mathrm{ct}}{\mathrm{d}}=1\)\" is placed in Equation (26), the V\({}_{\mathrm{peak}}\) value is obtained. \"\(\beta\cdot\frac{\mathrm{ct}}{\mathrm{d}}=1\)\" indicates the peak value of the induced stress recommended by IEEE standard 1410 [36,37]. Here, the \(\beta\) value indicates the relative velocity. Similarly, the actuation voltage was obtained from a line 15 m tall and 70 m away from the point where the LEMP fell Figure 13. The distance between two transmission poles, \(d=70\) m, is defined. The values were chosen because Turkish transmission systems typically use a distance between 40 and 70 m. This falls within the range of 15-40 m commonly used in Turkish transmission systems. The height of the pole, h = 15 m, is also defined. The lowest value was chosen to better understand the effect of the indirect pulse on the transmission line. The voltages concerning different \(\beta\) values (relative speed) were obtained for an LEMP current of 15 kA. In Figure 14, the peak value of the induced voltage according to the relative velocity is detailed. In particular, the validity of the model underlying the solutions and the approaches used in this model were analyzed, and the results in the literature were confirmed. The speed of the LEMP sprout affected the induced overvoltage value and the waveform, especially at the anterior slope of the wave. It was determined that the highest possible value of overvoltage induced in places far from the point where LEMP falls is proportional to the velocity of the LEMP sprout. Additionally, it is observed in Figure 14 that the speed has no effect at t = 0 on the induced overvoltage at a place near the impact point. Figure 11: Vectorial component for different LEMP currents for r = 100 m and z = 0 depending on the load distribution along the LEMP channel. (Solution for the function in Equation (22)). Figure 12: Magnetic field component for different LEMP currents for r = 100 m and z = 0 depending on the load distribution along the LEMP channel. (Solution for the function in Equation (23)).