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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 Solenoidal vector field ： ウィキペディア英語版 Solenoidal vector field In vector calculus a solenoidal vector field (also known as an incompressible vector field or a divergence free vector field ) is a vector field v with divergence zero at all points in the field: :$\backslash nabla\; \backslash cdot\; \backslash mathbf\; =\; 0.\backslash ,$ ==Properties== The fundamental theorem of vector calculus states that any vector field can be expressed as the sum of an irrotational and a solenoidal field. The condition of zero divergence is satisfied whenever a vector field v has only a vector potential component, because the definition of the vector potential A as: :$\backslash mathbf\; =\; \backslash nabla\; \backslash times\; \backslash mathbf$ automatically results in the identity (as can be shown, for example, using Cartesian coordinates): :$\backslash nabla\; \backslash cdot\; \backslash mathbf\; =\; \backslash nabla\; \backslash cdot\; (\backslash nabla\; \backslash times\; \backslash mathbf)\; =\; 0.$ The converse also holds: for any solenoidal v there exists a vector potential A such that $\backslash mathbf\; =\; \backslash nabla\; \backslash times\; \backslash mathbf.$ (Strictly speaking, this holds only subject to certain technical conditions on v, see Helmholtz decomposition.) The divergence theorem gives the equivalent integral definition of a solenoidal field; namely that for any closed surface, the net total flux through the surface must be zero: : where $d\backslash mathbf$ is the outward normal to each surface element. 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「Solenoidal vector field」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.