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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 Vector potential ： ウィキペディア英語版 Vector potential In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a ''scalar potential'', which is a scalar field whose gradient is a given vector field. Formally, given a vector field v, a ''vector potential'' is a vector A such that :$\backslash mathbf\; =\; \backslash nabla\; \backslash times\; \backslash mathbf.$ If a vector field v admits a vector potential A, then from the equality :$\backslash nabla\; \backslash cdot\; (\backslash nabla\; \backslash times\; \backslash mathbf)\; =\; 0$ (divergence of the curl is zero) one obtains :$\backslash nabla\; \backslash cdot\; \backslash mathbf\; =\; \backslash nabla\; \backslash cdot\; (\backslash nabla\; \backslash times\; \backslash mathbf)\; =\; 0,$ which implies that v must be a solenoidal vector field. ==Theorem== Let :$\backslash mathbf\; :\; \backslash mathbb\; R^3\; \backslash to\; \backslash mathbb\; R^3$ be a solenoidal vector field which is twice continuously differentiable. Assume that v(x) decreases sufficiently fast as ||x||→∞. Define :$\backslash mathbf\; (\backslash mathbf)\; =\; \backslash frac\; \backslash int\_\; \backslash frac)\}\; \backslash right\backslash |\}\; \backslash ,\; d^3\backslash mathbf.$ Then, A is a vector potential for v, that is, :$\backslash nabla\; \backslash times\; \backslash mathbf\; =\backslash mathbf.$ A generalization of this theorem is the Helmholtz decomposition which states that any vector field can be decomposed as a sum of a solenoidal vector field and an irrotational vector field. 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「Vector potential」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.