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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 Induction equation ： ウィキペディア英語版 Induction equation Induction equation, as one of the magnetohydrodynamic equations, is a partial differential equation with spatial and time variables that relates the magnetic and velocity fields of an electrically conductive fluid such as a plasma. This equation can be derived using the Maxwell's equations along with the so-called Ohm's law. Induction equation has also a major role in plasma physics and astrophysics specially in the magnetic dynamo theory. ==Mathematical statement== Maxwell's equations describing the Faraday's and Ampere's laws read $$ \vec\times\vec=-, and $$ \vec\times\vec=\mu_0\vec, where the displacement current has been neglected as it usually has small effects in astrophysical applications as well as in most of laboratory plasmas. Here, $\backslash vec$, and $\backslash vec$ are, respectively, electric and magnetic fields, and $\backslash vec$ is the electric current. The electric field can be related to the current density using the Ohm's law, $\backslash vec+\backslash vec\backslash times\backslash vec=\backslash vec/\backslash sigma$ where $\backslash vec$ is the velocity field, and $\backslash sigma$ is the electric conductivity of the fluid. Taking the time derivative of the first equation, and combining the result with the second one, yield $$ =\eta \nabla^2 \vec+\vec\times(\vec\times\vec), where $\backslash eta=1/\backslash mu\_0\backslash sigma$ is the magnetic diffusivity. (In the literature, the electrical resistivity, defined as $1/\backslash sigma$, is also sometimes called magnetic diffusivity, defined as $1/\backslash mu\_0\backslash sigma$, while they have different values in SI units.) The above equation is the induction equation for an electrically resistive fluid. If the fluid moves with a typical speed $V$ and a typical length scale $L$, then $$ \eta \nabla^2 \vec \sim , \vec\times (\vec\times \vec) \sim . The ratio of these quantities, which is a dimensionless parameter, is called the magnetic Reynolds number: $R\_m=$. 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「Induction 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.