\[\widetilde{\bf E}({\bf r}) \approx j \frac{\eta\beta}{4\pi} \int_{-L/2}^{+L/2} \hat{\bf \theta}' \widetilde{I}(z')~\left(\sin\theta'\right) \frac{e^{-j\beta \left|{\bf r}-\hat{\bf z}z'\right|}}{\lef...˜E(r)≈jηβ4π∫+L/2−L/2ˆθ′˜I(z′)(sinθ′)e−jβ|r−ˆzz′||r−ˆzz′|dz′ Since we have already assumed that r≫L (i.e., the distance to field points is much greater than the length of the dipole), the vector r is approximately parallel to the vector r−ˆzz′.
\[\widetilde{\bf E}({\bf r}) \approx j \frac{\eta\beta}{4\pi} \int_{-L/2}^{+L/2} \hat{\bf \theta}' \widetilde{I}(z')~\left(\sin\theta'\right) \frac{e^{-j\beta \left|{\bf r}-\hat{\bf z}z'\right|}}{\lef...˜E(r)≈jηβ4π∫+L/2−L/2ˆθ′˜I(z′)(sinθ′)e−jβ|r−ˆzz′||r−ˆzz′|dz′ Since we have already assumed that r≫L (i.e., the distance to field points is much greater than the length of the dipole), the vector r is approximately parallel to the vector r−ˆzz′.
