Question

Using the vector potential A and the procedure outlined in Section 3.6 of Chapter 3, derive the far-zone spherical electric and magnetic field components of a horizontal infinitesimal dipole placed at the origin of the coordinate system of Figure 4.1 Solution: Using (4-4), but for a horizontal infinitesimal dipole of uniform current directed along the y-axis, the corresponding vector potential can be written as uloleikr A = â 4πη with the corresponding spherical components, using the rectangular to spherical components transformation of (4-5), expressed as ulole ikr cos e sin Ag = A, cos 0 sin = 4TTr ulole-ikr cos A A, cos ø = 4πr Using (3-58a) and (3-58b), we can write the corresponding far-zone electric and magnetic field components as plole-ikr = -1- Eg-jaA cos e sin 4TTr oulole ik E-joA cos = 4πr oulle ikr cos 4πη Ep - H . ωμ1,le -ikr E [+ = -+ PH 4πηr cos esin Although the electric-field components, and thus the magnetic field components, take a different analytical form than (4-111), the patterns are the same. For Example 4.5, determine the polarization of the radiated far-zone fields (Eg, E) in the following planes: (a) 0° (b) ) = 90° (c) 0 = 90°

Answer 1

the E -ted components Fom the gven exomple Ex oLecason -AG uony= - wyTle-i casd Ep ayTo Lecosos= oEx YTY wye E4 YA8 lecsosnAd= -4 yoleTR% CoSO 9Ex o 90: Ed yLecassp -9E cesp E4 el