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- 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 symmetric 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 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). (en)
- Le principe de réciprocité, que l'on retrouve également dans d'autres domaines de la physique, s'exprime dans celui de l'électricité grâce à une relation générale entre les courants et les tensions observés aux interfaces de circuits passifs et linéaires. Ce théorème est une conséquence, en électromagnétisme, du théorème de réciprocité de Lorentz qui permet d'arriver à un résultat similaire par le biais de considérations plus fondamentales. (fr)
- Il principio di reciprocità nelle antenne, è una conseguenza delle equazioni di Maxwell ed è usato per dimostrare che esiste una relazione di tipo generale tra i parametri che caratterizzano il comportamento direzionale dell'antenna in trasmissione (TX) ed in ricezione (RX).Si ha che: dove è l'area efficace ovvero quel parametro per cui moltiplicare la densità di potenza per ottenere la potenza ricevuta in condizioni di adattamento. la lunghezza d'onda del segnale in trasmissione/ricezione, ovvero velocità della luce diviso frequenza di lavoro. guadagno dell'antenna. (it)
- Reciprocitetssatsen beskriver sambandet mellan den elektriska flödestätheten och de uppkomna elektromagnetiska fälten i enlighet med Maxwells ekvationer. (sv)
- Теоре́ма взаи́мности — название множества связанных друг с другом теорем, описывающих взаимное изменение гармонических по времени плотностей электрического тока (источников) и возникающих электромагнитных полей в уравнениях Максвелла для линейной изотропной и негиротропной среды. Вероятно, наиболее известной и общей из таких теорем является лемма Лоренца (и её частные случаи, такие как теорема Рэлея — Карсона), доказанная Хендриком Лоренцом в 1896 году после аналогичных результатов Рэлея и Гельмгольца применительно к звуковым волнам и свету соответственно. Проще говоря, лемма устанавливает, что взаимосвязь переменного тока и порождённого им электрического поля остаётся неизменной при смене мест точки, в которой протекает ток и точки, в которой наблюдается поле. (ru)
- 在电磁学中，互易定理是电磁场理论的重要定理。由洛伦兹首先发现了一个定义在闭合曲面上的电磁场公式。后来Rayleigh-Carson又进一步把定理发展称为我们今天看到的形式，定义在一个体积分上。 (zh)
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- Le principe de réciprocité, que l'on retrouve également dans d'autres domaines de la physique, s'exprime dans celui de l'électricité grâce à une relation générale entre les courants et les tensions observés aux interfaces de circuits passifs et linéaires. Ce théorème est une conséquence, en électromagnétisme, du théorème de réciprocité de Lorentz qui permet d'arriver à un résultat similaire par le biais de considérations plus fondamentales. (fr)
- Il principio di reciprocità nelle antenne, è una conseguenza delle equazioni di Maxwell ed è usato per dimostrare che esiste una relazione di tipo generale tra i parametri che caratterizzano il comportamento direzionale dell'antenna in trasmissione (TX) ed in ricezione (RX).Si ha che: dove è l'area efficace ovvero quel parametro per cui moltiplicare la densità di potenza per ottenere la potenza ricevuta in condizioni di adattamento. la lunghezza d'onda del segnale in trasmissione/ricezione, ovvero velocità della luce diviso frequenza di lavoro. guadagno dell'antenna. (it)
- Reciprocitetssatsen beskriver sambandet mellan den elektriska flödestätheten och de uppkomna elektromagnetiska fälten i enlighet med Maxwells ekvationer. (sv)
- 在电磁学中，互易定理是电磁场理论的重要定理。由洛伦兹首先发现了一个定义在闭合曲面上的电磁场公式。后来Rayleigh-Carson又进一步把定理发展称为我们今天看到的形式，定义在一个体积分上。 (zh)
- 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 symmetric operators from linear algebra, applied to electromagnetism. Reciprocity is useful in optics, which (apart from quantum effects) can be expressed in terms of classical electromagnetism, but also in terms of radiometry. (en)
- Теоре́ма взаи́мности — название множества связанных друг с другом теорем, описывающих взаимное изменение гармонических по времени плотностей электрического тока (источников) и возникающих электромагнитных полей в уравнениях Максвелла для линейной изотропной и негиротропной среды. (ru)
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