# An Approach for Modelling Harnesses in the Extreme near Field for Low Frequencies
## 2 Near-Field Approximations Very Close to the Dipole Source
### Considerations for Observation Distances Comparable to the Cable's Length
It is clear, however, that segmentation has a major impact for values of _ratio_ below 4, while for values of _ratio_ above 4, the Single Dipole Case and the Segmented Cable Case (for \(N\) = 50,000) converge. Moreover, Figure 4 suggests that significantly fewer segments (\(N\) = 50) are actually enough to achieve an accuracy better than 99.9%. Figure 4: Comparison of the real and imaginary parts of the electric field component \(E_{x}\) versus the _ratio_ of the measurement distance to the cable length, for the Single Dipole Case (x marks) and the Segmented Dipole Case for \(N\) = 50 segments (dashed lines). Figure 3: Comparison of the magnitude of the electric field \(({E_{x}}^{2}+{E_{y}}^{2}+{E_{z}}^{2})^{1/2}\) versus the _ratio_ of the measurement distance to the cable length, for \(N\) = 0 (straight blue line), 5 (bulleted red line), 50 (x marks), and 50,000 (dashed line) segments. Accordingly, the real part of the electric field is many orders smaller than the imaginary, thus all the analysis is based on the imaginary part (which is dominant in magnitude). Thus, in this case, the segmentation is mandatory and the field result differentiates from the Single Dipole Case where one dipole is considered. As a result, \(N=50\) is considered a sufficiently safe choice for the ratio parameter evaluation. Figures 4-6 showcases the comparison between the Single Dipole Case and the corresponding Segmented Dipole Case with \(N=50\) subparts. This comparison has been performed for different values of the _ratio_ parameter to identify the minimum observation distance (compared to the cable length) for which the source segmentation is not required anymore. Moreover, the calculations make apparent that for distances four times larger than the cable length (_ratio_ > 4), the difference between the Single Dipole Case and the Segmented Cable Case is less than 5%. This percentage is inversely proportional to the _ratio_, so it decreases when the _ratio_ increases. The same remarks also apply to the \(E_{y}\) and \(E_{z}\) electric field components. Figure 5: Comparison of the real and imaginary parts of the electric field component \(E_{x}\) versus the _ratio_ of the measurement distance to the cable length, for the Single Dipole Case (circles), the Segmented Dipole Case for \(N=50\) segments (dashed lines), and the Single Dipole Case with Near Field Approximation (x marks). Figure 6: Comparison of the real and imaginary parts of the electric field component \(E_{x}\) versus the _ratio_ of the measurement distance to the cable length, for the Segmented Cable Case (star marks) and the Segmented Cable Case with Near Field Approximation with \(N=50\) segments (dashed lines). Figure 3 reveals that the convergence of the electric field calculation is obtained for segmentation numbers \(N\) less than 50. In fact, the field convergence is improved by less than 0.1% when \(N\) increases from 20 to 50. However, for the rest of the cases presented herein, and in order to maximize the accuracy, we have used \(N=50\) segments. The above considerations have also been confirmed for the 90 kHz frequency. Additional calculations, which were carried out considering different observation distances (r = 4 m and r = 8 m) but with the same _ratio_ values, have verified the aforementioned conclusions. Thus, the current study proposes a practical rule for modeling harnesses either with a single Hertzian dipole or with a set of multiple Hertzian dipoles arising after the appropriate segmentation process, when the observation point is in close proximity to the source.