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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 Ampère's force law ： ウィキペディア英語版 Ampère's force law In magnetostatics, the force of attraction or repulsion between two current-carrying wires (see first figure below) is often called Ampère's force law. The physical origin of this force is that each wire generates a magnetic field, as defined by the Biot–Savart law, and the other wire experiences a magnetic force as a consequence, as defined by the Lorentz force. ==Equation== The best-known and simplest example of Ampère's force law, which underlies the definition of the ampere, the SI unit of current, states that the force per unit length between two straight parallel conductors is ::$\backslash frac\; =\; 2\; k\_A\; \backslash frac$, where ''k''A is the magnetic force constant from the Biot–Savart law, ''Fm/L'' is the total force on either wire per unit length of the shorter (the longer is approximated as infinitely long relative to the shorter), ''r'' is the distance between the two wires, and ''I''1, ''I''2 are the direct currents carried by the wires. This is a good approximation if one wire is sufficiently longer than the other that it can be approximated as infinitely long, and if the distance between the wires is small compared to their lengths (so that the one infinite-wire approximation holds), but large compared to their diameters (so that they may also be approximated as infinitely thin lines). The value of ''k''A depends upon the system of units chosen, and the value of ''k''A decides how large the unit of current will be. In the SI system, ::$k\_A\; \backslash \; \backslash overset\}\backslash \; \backslash frac$ with μ0 the magnetic constant, ''defined'' in SI units as〔(''BIPM definition'' )〕 ::$\backslash mu\_0\; \backslash \; \backslash overset\}\; \backslash \; 4\; \backslash pi\; \backslash times\; 10^$ N / A2. Thus, in vacuum, :''the force per meter of length between two parallel conductors – spaced apart by 1 m and ''each'' carrying a current of 1 A – is exactly'' :: $\backslash displaystyle\; 2\; \backslash times\; 10^$ N / m. The general formulation of the magnetic force for arbitrary geometries is based on iterated line integrals and combines the Biot–Savart law and Lorentz force in one equation as shown below. 〔The integrand of this expression appears in the official documentation regarding definition of the ampere (BIPM SI Units brochure, 8th Edition, p. 105 )〕 :〔(Ampère's Force Law ) '' Scroll to section "Integral Equation" for formula. ''〕 :$\backslash vec\_\; =\; \backslash frac\; \backslash int\_\; \backslash int\_\; \backslash frac\; \backslash \; (I\_2\; d\; \backslash vec\_2\; \backslash \; \backslash mathbf\; \backslash \; \backslash hat\; )\}$, where *$\backslash vec\_$ is the total force felt by wire 1 due to wire 2 (usually measured in newtons), *''I''1 and ''I''2 are the currents running through wires 1 and 2, respectively (usually measured in amperes), *The double line integration sums the force upon each element of wire 1 due to the magnetic field of each element of wire 2, *$d\; \backslash vec\_1$ and $d\; \backslash vec\_2$ are infinitesimal vectors associated with wire 1 and wire 2 respectively (usually measured in metres); see line integral for a detailed definition, *The vector $\backslash hat$ is the unit vector pointing from the differential element on wire 2 towards the differential element on wire 1, and ''|r|'' is the distance separating these elements, *The multiplication × is a vector cross product, *The sign of ''I''n is relative to the orientation $d\; \backslash vec\_n$ (for example, if $d\; \backslash vec\_1$ points in the direction of conventional current, then ''I''1>0). To determine the force between wires in a material medium, the magnetic constant is replaced by the actual permeability of the medium. 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「Ampère's force law」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.