Q4Electromagnetics Waves

For a Hertzian (infinitesimal) dipole of length dl carrying current I0 at angular frequency ω, the exact field solution contains terms varying as 1/r, 1/r², and 1/r³ from the source. The relative importance of these terms divides the space around the antenna into three distinct field regions, most simply demarcated for a Hertzian dipole by the radial distance r compared with λ/2π (the point where the 1/r and 1/r² terms are equal in magnitude).

Near field (r ≪ λ/2π), reactive/induction region: dominated by the 1/r² and 1/r³ terms. The 1/r³ term is the electrostatic-like field of the instantaneous dipole moment (as if the source were a static dipole), and the 1/r² term is the induction (quasi-magnetostatic) field analogous to the Biot-Savart field of a slowly time-varying current element. In this region E and H are in approximate phase quadrature (90° out of phase), so the time-average Poynting vector (real power flow) is essentially zero — energy oscillates back and forth between the antenna and the surrounding field each half-cycle rather than propagating away, exactly like the reactive field of a capacitor or inductor storing and releasing energy. Properties: rapid (1/r², 1/r³) decay, reactive (non-propagating) power, field pattern strongly resembles the static dipole/current-element pattern, and this is the region exploited by near-field/inductive wireless power transfer and by near-field probes.

Far field (r ≫ λ/2π, typically r > 2D²/λ for a finite antenna of size D), radiation region: dominated exclusively by the 1/r term, since the faster-decaying 1/r² and 1/r³ terms become negligible at large r. Here E and H are in exact time phase, mutually perpendicular, and both perpendicular to the radial direction r̂ (a locally plane-wave-like TEM structure), related by E/H = η0 = 377 Ω (free-space intrinsic impedance), and the radiation pattern (the angular shape of the field, e.g., the sin θ pattern of the Hertzian dipole) becomes independent of r — it is only in this region that a fixed, r-independent 'radiation pattern' is meaningfully defined. The time-average Poynting vector is real and directed radially outward, S = |E|²/(2η0) r̂, representing genuine, permanently radiated power that never returns to the antenna, decaying as 1/r² in power density (consistent with 1/r field amplitude) exactly as required for total radiated power (∝ S×4πr²) to remain constant with distance — this is the region in which all practical antenna radiation-pattern, gain and directivity measurements are made.