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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 Electric-field integral equation ： ウィキペディア英語版 Electric-field integral equation The electric-field integral equation is a relationship that allows the calculation of an electric field intensity (E) generated by an electric current distribution (J). ==Derivation== When all quantities in the frequency domain are considered, a time-dependency $e^\backslash ,$ that is suppressed throughout is assumed. Beginning with the Maxwell equations relating the electric and magnetic field an assuming linear, homogeneous media with permeability $\backslash epsilon\backslash ,$ and permittivity $\backslash mu\backslash ,$: :$\backslash nabla\; \backslash times\; \backslash textbf\; =\; -j\; \backslash omega\; \backslash mu\; \backslash textbf\backslash ,$ :$\backslash nabla\; \backslash times\; \backslash textbf\; =\; j\; \backslash omega\; \backslash epsilon\; \backslash textbf\; +\; \backslash textbf\backslash ,$ Following the third equation involving the divergence of H :$\backslash nabla\; \backslash cdot\; \backslash textbf\; =\; 0\backslash ,$ by vector calculus we can write any divergenceless vector as the curl of another vector, hence :$\backslash nabla\; \backslash times\; \backslash textbf\; =\; \backslash textbf\backslash ,$ where A is called the magnetic vector potential. Substituting this into the above we get :$\backslash nabla\; \backslash times\; (\backslash textbf\; +\; j\; \backslash omega\; \backslash mu\; \backslash textbf)\; =\; 0\backslash ,$ and any curl-free vector can be written as the gradient of a scalar, hence :$\backslash textbf\; +\; j\; \backslash omega\; \backslash mu\; \backslash textbf\; =\; -\; \backslash nabla\; \backslash Phi$ where $\backslash Phi$ is the electric scalar potential. These relationships now allow us to write :$\backslash nabla\; \backslash times\; \backslash nabla\; \backslash times\; \backslash textbf\; -\; k^\backslash textbf\; =\; \backslash textbf\; -\; j\; \backslash omega\; \backslash epsilon\; \backslash nabla\; \backslash Phi\; \backslash ,$ where $k\; =\; \backslash omega\; \backslash sqrt$, which can be rewritten by vector identity as :$\backslash nabla\; (\backslash nabla\; \backslash cdot\; \backslash textbf)\; -\; \backslash nabla^\; \backslash textbf\; -\; k^\backslash textbf\; =\; \backslash textbf\; -\; j\; \backslash omega\; \backslash epsilon\; \backslash nabla\; \backslash Phi\; \backslash ,$ As we have only specified the curl of A, we are free to define the divergence, and choose the following: :$\backslash nabla\; \backslash cdot\; \backslash textbf\; =\; -\; j\; \backslash omega\; \backslash epsilon\; \backslash Phi\; \backslash ,$ which is called the Lorenz gauge condition. The previous expression for A now reduces to :$\backslash nabla^\; \backslash textbf\; +\; k^\backslash textbf\; =\; -\backslash textbf\backslash ,$ which is the vector Helmholtz equation. The solution of this equation for A is :$\backslash textbf(\backslash textbf)\; =\; \backslash frac\; \backslash iiint\; \backslash textbf(\backslash textbf^)\; \backslash \; G(\backslash textbf,\; \backslash textbf^)\; \backslash \; d\backslash textbf^\; \backslash ,$ where $G(\backslash textbf,\; \backslash textbf^)\backslash ,$ is the three-dimensional homogeneous Green's function given by :$G(\backslash textbf,\; \backslash textbf^)\; =\; \backslash frac^|\}\}^|\}\backslash ,$ We can now write what is called the electric field integral equation (EFIE), relating the electric field E to the vector potential A :$\backslash textbf\; =\; -j\; \backslash omega\; \backslash mu\; \backslash textbf\; +\; \backslash frac\; \backslash nabla\; (\backslash nabla\; \backslash cdot\; \backslash textbf)\backslash ,$ We can further represent the EFIE in the dyadic form as :$\backslash textbf\; =\; -j\; \backslash omega\; \backslash mu\; \backslash int\_V\; d\; \backslash textbf^\; \backslash textbf(\backslash textbf,\; \backslash textbf^)\; \backslash cdot\; \backslash textbf(\backslash textbf^)\; \backslash ,$ where $\backslash textbf(\backslash textbf,\; \backslash textbf^)\backslash ,$ here is the dyadic homogeneous Green's Function given by :$\backslash textbf(\backslash textbf,\; \backslash textbf^)\; =\; \backslash frac\; \backslash left(\backslash textbf+\backslash frac\; \backslash right)\; G(\backslash textbf,\; \backslash textbf^)\; \backslash ,$ 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「Electric-field integral equation」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.