翻訳と辞書 Words near each other ・ Quadruple Alliance (1815) ・ Quadruple bond ・ Quadruple champion ・ Quadruple D ・ Quadruple jump controversy ・ Quadruple play ・ Quadruple product ・ Quadruple reed ・ Quadruple track ・ Quadruple-precision floating-point format ・ Quadruple-stranded DNA ・ Quadruplex ・ Quadruplex telegraph ・ Quadruplex videotape ・ Quadruply clad fiber ・ Quadrupole ・ Quadrupole formula ・ Quadrupole ion trap ・ Quadrupole magnet ・ Quadrupole mass analyzer ・ Quadrupole splitting ・ Quadrus ・ Quadrus cerialis ・ Quadstone Paramics ・ Quadtree ・ Quadtrine Hill ・ Quadwave ・ Quadyuk Island ・ Quadzilla ・ Quaere Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quadrupole ： ウィキペディア英語版 Quadrupole A quadrupole or quadrapole is one of a sequence of configurations of—for example—electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure reflecting various orders of complexity. ==Mathematical definition== The quadrupole moment tensor Q is a rank-two tensor (3x3 matrix) and is traceless (i.e. $Q\_+Q\_+Q\_=0$). The quadrupole moment tensor has thus 9 components, but because of the symmetry and zero-trace property, only 5 of these are independent. For a discrete system of point charges (or masses in the case of a gravitational quadrupole), each with charge $q\_$ (or mass $m\_$) and position $\backslash vec=(r\_,r\_,r\_)$ relative to the coordinate system origin, the components of the Q matrix are defined by: $Q\_=\backslash sum\_l\; q\_l(3r\_\; r\_-\backslash |\backslash vec\backslash |^2\backslash delta\_)$. The indices $i,j$ run over the Cartesian coordinates $x,y,z$ and $\backslash delta\_$ is the Kronecker delta. For a continuous system with charge density (or mass density) $\backslash rho(x,y,z)$, the components of Q are defined by integral over the Cartesian space r: $Q\_=\backslash int\backslash ,\; \backslash rho(3r\_i\; r\_j-\backslash |\backslash vec\backslash |^2\backslash delta\_)\backslash ,\; d^3\backslash bold$ As with any multipole moment, if a lower-order moment (monopole or dipole in this case) is non-zero, then the value of the quadrupole moment depends on the choice of the coordinate origin. For example, a dipole of two opposite-sign, same-strength point charges (which has no monopole moment) can have a nonzero quadrupole moment if the origin is shifted away from the center of the configuration (exactly between the two charges); or the quadrupole moment can be reduced to zero with the origin at the center. In contrast, if the monopole and dipole moments vanish, but the quadrupole moment does not (e.g., four same-strength charges, arranged in a square, with alternating signs), then the quadrupole moment is coordinate independent. If each charge is the source of a "$1/r$" field, like the electric or gravitational field, the contribution to the field's potential from the quadrupole moment is: :$V\_q(\backslash mathbf)=\backslash frac\; \backslash sum\_\; \backslash frac\; Q\_\backslash ,\; n\_i\; n\_j\backslash \; ,$ where R is a vector with origin in the system of charges and n is the unit vector in the direction of R. Here, $k$ is a constant that depends on the type of field, and the units being used. The factors $n\_i,\; n\_j$ are components of the unit vector from the point of interest to the location of the quadrupole moment. 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「Quadrupole」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.