A center-fed half-wave dipole is analyzed by assuming which current distribution along its length?

In the far-field approximation for a linear antenna, the distance from a current element to a distant point P is simplified as R ≈ r − z cosθ. What additional approximation is typically made for the denominator when integrating for Az at large r?

For a centre-fed dipole with total length l = 2h = λ/2 and phase constant β = 2π/λ, which trigonometric identities convert sinβ(h ± z) into functions of βz in the Az derivation?

During simplification, the term $$e^{jβz cosθ} + e^{−jβz cosθ}$$ appears inside the integral for Az. Which identity is used to replace this sum, and what does it become?

After applying the product-to-sum identity $$2 \cos A \cos B = \cos(A+B) + \cos(A−B)$$ and integrating from 0 to h with $$\beta h = \frac{\pi}{2}$$ , which final angular factor multiplies $$\mu I_m e^{-j\beta r}/(2\pi\beta r)$$ in Az for the half-wave dipole far field?

In free space, the intrinsic impedance η relates the magnitudes of the far‑field components as η = |Eθ|/|Hφ|. What numerical value of η is used to compute Eθ from Hφ in the notes?

The maximum time‑average power density (W/m²) radiated by a short dipole is found using the Poynting vector. Which expression is used for the peak value before averaging?

For the given short dipole derivation, the radiation resistance is taken as which value?

Using Aem = V²/(4S Rrad) with V = Eλ/π and S = E²/η, the maximum effective aperture is obtained as Aem ≈ 0.13λ². What directivity value D follows from D = 4πAem/λ²?