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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: : ==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: : automatically results in the identity (as can be shown, for example, using Cartesian coordinates): : The converse also holds: for any solenoidal v there exists a vector potential A such that (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 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
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