I ( - z/v - r1 /c)d i ( - z/v - dz/v - r2

I ( – z/v – r1 /c)d i ( – z/v – dz/v – r2 /c)d z/v-r /c i (z) z/v-dz/v-r1 /c 1 destat (t) = – ar1 – ar2 2 two 4 o r1 r2 Appendix B.two. Electromagnetic Fields Generated by the Lightning Channel The radiation and static terms in Equation (8a ) follow directly in the above two equations A15 and A16 after the equations are lowered for the condition that dz is infinitesimal and summing up the contribution from all the channel elements by performing the integration along the channel. Nevertheless, let us maintain the above equations inside the existing kind and replace the integration along the channel by a summation. Let us take into account the radiation field. When we take the summation starting in the first element located at the bottom of the channel, a single can see directly that the radiation coming in the best from the first element will likely be cancelled off using the radiation coming from the bottom in the second element, the radiation coming in the leading from the second element will be cancelled off with all the radiation coming from the bottom with the third element, and so forth. As a result, at any point in space, only the radiation term coming in the bottom from the initially element will survive(A16)Atmosphere 2021, 12,13 ofduring the summation. Thus, the radiation field at the Alprenolol Purity & Documentation surface of a perfectly conducting ground is given by v i (t – z/v – d/c) erad = – az . (A17) d 2 o c2 Observe that within the above case, r1 D , sin 1 as well as a -az . That is identical to the radiation field in Equation (9a ). Now, let us look at the static term. As inside the radiation field, any time you take the summation, only the term corresponding for the bottom of the initial element will survive. On the other hand, when we take into account the truth that the lightning channel is positioned above a perfectly conducting ground, this static term will cancel off with the corresponding term connected together with the image from the element within the perfectly conducting ground plane. As a result, the total static field will develop into equal to zero. That’s, estat = 0. (A18) This evaluation shows that all of the terms of Equation (8a ) are identical towards the corresponding terms in Equation (9a ) and that these two equations are identical to one another. Just to illustrate this further, we have calculated the electric field at one hundred m distance from a lightning channel using Equations (8a ) and (9a ). The different components as well as the total field obtained from Equations (8a ) and (9a ) 15 depicted in Figure A2. Note which can be 14 of as illustrated above, the three field terms are identical in each formulations.Atmosphere 2021, 12,(a)(b)Figure A2. Plot of the field components connected with (a) Equation (8a ) and (b) Equation (9a ). Figure A2. Plot from the strike point of a lightning return stroke simulated The electric field is calculated at 100 m with the field components related with (a) Equation (8a ) and (b) Equation (9a ). by the transmission line model. The existing in the channel base is represented by the analytical of a lightning return stroke simulated The electric field is calculated at 100 m in the strike point expression given by Nucci et al. [17] to represent subsequent return strokes. The return stroke speed by the transmission line model. The current in the channel base is represented by the analytical used inside the calculation is 1.five 108 m/s.
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