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Solenoidal vector field
In vector calculus a solenoidal vector field is a vector field v with divergence zero:
Additional recommended knowledge
This condition is satisfied whenever v has a vector potential, because if
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 S, the net total flux through the surface must be zero:
where is the outward normal to each surface element.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Solenoidal_vector_field". A list of authors is available in Wikipedia.|