Evaluate the time-average Poynting vector, = (1/2)Re E s à H s for the magnetic dipole antenna in the far zone, in which all terms

Evaluate the time-average Poynting vector, = (1/2)Re E_s× H^ˆ—_sfor the magnetic dipole antenna in the far zone, in which all terms of order 1/r²and 1/r⁴are neglected in Eqs. (48), (49), and (50). Compare your result to the far-zone power density of the Hertzian dipole, Eq. (26). In this comparison, and assuming equal current amplitudes, what relation between loop radius, a, and dipole length, d, would result in equal radiated powers from the two devices?

Eqs. (48)

Eqs. (26)

Eqs. (49)

Eqs. (50)

 

, (') bk Eps = -j 4r 1 1/2 sin exp[- kr - ) 1+ (kr)2 2. | | = S, = 1 ( Iokd n sin? e 2 4ar