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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Electrokinematics theorem ： ウィキペディア英語版 Electrokinematics theorem The electrokinematics theorem〔Pellegrini, B. (1986), "Electric charge motion, induced current, energy balance, and noise", Phys. Rev. B 34: 5921-5924.〕〔Pellegrini, B.(1993), "Extension of the electrokinematics theorem to the electromagnetic field and quantum mechanics", Il Nuovo Cimento 15 D: 855–879.〕〔Pellegrini, B.(1993), "Elementary application of quaantum-electrokinematics theorem to the electromagnetic field and quantum mechanics", Il Nuovo Cimento 15 D: 881-896.〕 connects the velocity and the charge of carriers moving inside an arbitrary volume to the currents, voltages and power on its surface through an arbitrary irrotational vector. Since it contains, as a particular application, the Ramo-Shockley theorem,〔Ramo, S.(1939), "Currents induced by electron motion", Proc. IRE 27: 584–585.〕〔Shockley, W. (1938), Currents to conductors induced by a moving point charge, J. App. Phys. 9: 635-636.〕 the electrokinematics theorem is also known as Ramo-Shockly-Pellegrini theorem. ==Statement== To introduce the electrokinematics theorem let us first list a few definitions: ''qj'', ''rj'' and ''vj'' are the electric charge, position and velocity, respectively, at the time t of the ''j''th charge carrier; $A\_$, $E=-\backslash nabla\; A\_$ and $\backslash varepsilon$ are the electric potential, field, and permittivity, respectively, $J\_$, $J\_=\backslash varepsilon\; \backslash partial\; E/\; \backslash partial\; t$ and $J=J\_+J\_$ are the conduction, displacement and, in a 'quasi-electrostatic' assumption, total current density, respectively; $F=-\backslash nabla\; \backslash Phi$ is an arbitrary irrotational vector in an arbitrary volume $\backslash Omega$ enclosed by the surface S, with the constraint that $\backslash nabla\; (\backslash varepsilon\; F)=0$. Now let us integrate over $\backslash Omega$ the scalar product of the vector $F$ by the two members of the above-mentioned current equation. Indeed, by applying the divergence theorem, the vector identity $a\backslash cdot\backslash nabla\backslash gamma=\backslash nabla\backslash cdot(\backslash gamma\; a)-\backslash gamma\backslash nabla\backslash cdot\; a$, the above-mentioned constraint and the fact that $\backslash nabla\backslash cdot\; J=0$, we obtain the electrokinematics theorem in the first form :$-\backslash int\_\; \backslash Phi\; J\backslash cdot\; dS=\backslash int\_J\_\backslash cdot\; Fd^r-\backslash int\_\backslash varepsilon\backslash fracF\backslash cdot\; dS$ , which, taking into account the corpuscular nature of the current $J\_=\backslash sum\_^\; q\_\backslash delta(r-r\_)v\_$, where $\backslash delta(r-r\_)$ is the Dirac delta function and ''N(t)'' is the carrier number in $\backslash Omega$ at the time ''t'', becomes :$-\backslash int\_\; \backslash Phi\; J\backslash cdot\; dS=\backslash sum\_^\; q\_v\_\backslash cdot\; F(r\_)-\backslash int\_\backslash varepsilon\backslash fracF\backslash cdot\; dS$ . A component $A\_()=V\_(t)\backslash psi\_(r)$ of the total electric potential $A\_=A\_+A\_$ is due to the voltage $V\_(t)$ applied to the ''k''th electrode on ''S'', on which $\backslash psi\_(r)=1$ (and with the other boundary conditions $\backslash psi\_(r)=\backslash psi\_(\backslash infty)=0$ on the other electrodes and for $r\; \backslash to\; \backslash infty$), and each component $A\_()$ is due to the ''j''th charge carrier ''qj'' , being $A\_()=0$ for $r$ and $r\_j(t)$ over any electrode and for $r\; \backslash to\; \backslash infty$. Moreover, let the surface ''S'' enclosing the volume $\backslash Omega$ consist of a part $S\_=\backslash sum\_^S\_$ covered by ''n'' electrodes and an uncovered part $S\_R$. According to the above definitions and boundary conditions, and to the superposition theorem, the second equation can be split into the contributions :$-\backslash int\_\backslash cdot\; dS=\backslash sum\_^\; q\_v\_\backslash cdot\; F(r\_)+\backslash sum\_^\backslash int\_\}-\backslash fracF)\backslash cdot\; dS$ , :$-\backslash int\_\backslash cdot\; dS=\backslash sum\_^n\; \backslash int\_\}\; \backslash cdot\; dS-\backslash sum\_^n\; \backslash int\_\backslash varepsilon\; \backslash frac\; F\backslash cdot\; dS$, relative to the carriers and to the electrode voltages, respectively, $M(t)$ being the total number of carriers in the space, inside and outside $\backslash Omega$, at time ''t'', $E\_=-\backslash nabla\; A\_$ and $E\_=-\backslash nabla\; A\_$. The integrals of the above equations account for the displacement current, in particular across $S\_R$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Electrokinematics theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.