Reciprocity (electromagnetism) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-01-13

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Reciprocity_(electromagnetism)


00:02:23 1 Lorentz reciprocity
00:08:37 2 Reciprocity for electrical networks
00:16:25 3 Conditions and proof of Lorentz reciprocity
00:38:01 3.1 Surface-term cancellation
00:44:09 3.2 Reciprocity and the Green's function
00:46:52 3.3 Lossless magneto-optic materials
00:50:56 3.4 Generalization to non-symmetric materials
00:53:00 3.5 Exceptions to reciprocity
00:53:29 4 Feld-Tai reciprocity
00:55:43 5 Optical reciprocity in radiometric terms
00:57:58 6 Green's reciprocity



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SUMMARY
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This page is about reciprocity theorems in classical electromagnetism.  See also Reciprocity theorem (disambiguation) for unrelated reciprocity theorems, and Reciprocity (disambiguation) for more general usages of the term.In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources) and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints.  Reciprocity is closely related to the concept of Hermitian operators from linear algebra, applied to electromagnetism.
Perhaps the most common and general such theorem is Lorentz reciprocity (and its various special cases such as Rayleigh-Carson reciprocity),  named after work by Hendrik Lorentz in 1896 following analogous results regarding sound by Lord Rayleigh and light by Helmholtz (Potton, 2004). Loosely, it states that the relationship between an oscillating current and the resulting electric field is unchanged if one interchanges the points where the current is placed and where the field is measured.  For the specific case of an electrical network, it is sometimes phrased as the statement that voltages and currents at different points in the network can be interchanged.  More technically, it follows that the mutual impedance of a first circuit due to a second is the same as the mutual impedance of the second circuit due to the first.
Reciprocity is useful in optics, which (apart from quantum effects) can be expressed in terms of classical electromagnetism, but also in terms of radiometry.
There is also an analogous theorem in electrostatics, known as Green's reciprocity, relating the interchange of electric potential and electric charge density.
Forms of the reciprocity theorems are used in many electromagnetic applications, such as analyzing electrical networks and antenna systems.  For example, reciprocity implies that antennas work equally well as transmitters or receivers, and specifically that an antenna's radiation and receiving patterns are identical.  Reciprocity is also a basic lemma that is used to prove other theorems about electromagnetic systems, such as the symmetry of the impedance matrix and scattering matrix, symmetries of Green's functions for use in boundary-element and transfer-matrix computational methods, as well as orthogonality properties of harmonic modes in waveguide systems (as an alternative to proving those properties directly from the symmetries of the eigen-operators).