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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 : If a vector field v admits a vector potential A, then from the equality : (divergence of the curl is zero) one obtains : which implies that v must be a solenoidal vector field. ==Theorem== Let : be a solenoidal vector field which is twice continuously differentiable. Assume that v(x) decreases sufficiently fast as ||x||→∞. Define : Then, A is a vector potential for v, that is, : 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
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