Metric manipulations, we obtain1 Ez (t) = – two 0 L 0 cos i (t -z/v) 1 dz – two 0 v r2 1 – 2 0 L 0 L 0 cos i (t -z/v) dz crv t(7)1 i (t -z/v) dz t c2 rNote that all of the field terms are now provided with regards to the channel-base present. 4.3. Discontinuously Moving Charge Procedure Within the case on the transmission line model, the field equations pertinent to this procedure can be written as follows.LEz,rad (t) = -0 Ldz 2 o c2 ri (t ) sin2 tL+0 Ldz two o c2 r2v sin2 cos i (t r (1- v cos ) c v cos sin2 i (t (1- v cos ) c)(8a)-dz 2 o c2 rv2 sin4 i (t rc(1- v cos )2 c) +dz 2 o c2 r)Atmosphere 2021, 12,7 ofLEz, vel (t) = -i (t )dz 2 o r2 1 -L dz 2 o r2 v Glutarylcarnitine Autophagy ccoscos 1 – v ccos v i (t1-v2 c(8b)Ez,stat (t) = -0 L- cos i (t ) + ct r)(8c)+dz 2 o r3 sin2 -2i dtb4.4. Constantly Moving Charge Process In the case in the transmission line model, it can be a easy matter to show that the field expressions minimize to i (t )v (9a) Ez,rad = – two o c2 dLdzi (t – z/v) 1 – two o r2 1-v cEz,vel =cosv2 c2cos 1 – v c(9b) (9c)Ez,stat =Note that in the case on the transmission line model, the static term and also the initially 3 terms of your radiation field cut down to zero. 5. Discussion Based on the Lorentz approach, the continuity equation technique, the discontinuously moving charge technique, along with the continuously moving charge approach, we’ve 4 expressions for the electric field generated by return strokes. They are the four independent approaches of getting electromagnetic fields in the return stroke readily available inside the literature. These expressions are given by Equations (1)4a ) for the common case and Equations (6)9a ), respectively, for any return stroke represented by the transmission line model. Despite the fact that the field expressions obtained by these distinct procedures appear distinctive from every single other, it truly is probable to show that they can be transformed into each other, demonstrating that the apparent non-uniqueness of your field elements is resulting from the unique approaches of summing up the contributions for the total field arising from the accelerating, moving, and stationary charges. Very first take into account the field expression obtained using the discontinuously moving charge procedure. The expression for the total electric field is offered by Equation (8a ). Within this expression, the electric fields generated by accelerating charges, uniformly moving charges, and stationary charges are provided separately as Equation (8a ), respectively. This equation has been derived and studied in detail in [10,12], and it can be shown that Equation (8a ) is analytically identical to Equation (six) derived using the Lorentz condition or the dipole procedure. Basically, this was proved to become the case for any common current distribution (i.e., for the field expressions offered by Equations (1) and (3a )) in these publications. On the other hand, when converting Equation (8a ) into (six) (or (3a ) into (1)), the terms corresponding to distinctive underlying physical processes need to be combined with every single other, and also the one-to-one correspondence in between the electric field terms plus the physical processes is lost. Additionally, observe also that the speed of propagation from the existing appears only inside the integration limits in Equation (1) (or (6)), as opposed to Equation (8a ) (or (3a )), in which the speed seems also directly within the integrand. Let us now look at the field expressions obtained working with the continuity equation procedure. The field expression is provided by Equation (7). It is doable to show that this equation is ana.