in the \"far field\" region, show that the electric field intensity of a linear
ID: 1925012 • Letter: I
Question
in the "far field" region, show that the electric field intensity of a linear electric quadrupole decays much faster in space than 1/R3 for the electric field intensity produced by an electric dipole and 1/R2 for an electric monopole.
Explanation / Answer
For a far-field region it should satisfy three conditions.[citation needed] R > (2D^2/?) R >> D R >> ? where D is the diameter or length of an object/antenna and R is the distance from it The "far-field" extends outward to infinity, beginning about two wavelengths distance from an electromagnetically "short" antenna[citation needed]. Antennas are mostly used to communicate wirelessly for long distances using far-fields. This is the main region of operation. A "short" antenna is defined in this context as one that is shorter than half the wavelength of the radiation it emits[citation needed] (see rules for longer antennas, below). The far-field is the region in which the field acts as "normal" electromagnetic radiation. The power of this radiation decreases as the square of distance from the antenna, and absorption of the radiation has no effect on the transmitter. The "far-field region" is the region outside the near-field region, where the angular field distribution is in essence independent of distance from the source. In the far-field, the shape of the antenna pattern is independent of distance. If the source has a maximum overall dimension D (aperture width) that is large compared to the wavelength ?, the far-field region is commonly taken to exist at distances from the source, greater than Fresnel parameter S = D2/(4?), S > 1. For a beam focused at infinity, the far-field region is sometimes referred to as the "Fraunhofer region". Other synonyms are "far-field", "far-zone", and "radiation field". Any electromagnetic radiation consists of an electric field component E and a magnetic field component H. In the far-field, the relationship between the electric field component E and the magnetic component H is that characteristic of any freely propagating wave, where (in units where c = 1) E is equal to H at any point in space.
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