PlanetMath: solenoidal field

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solenoidal field

(Definition)

A solenoidal vector field is one that satisfies

$\displaystyle \nabla \cdot\mathbf{B}= 0$

at every point where the vector field $\mathbf{B}$ is defined. Here $\nabla \cdot\mathbf{B}$ is the divergence.

This condition actually implies that there exists a vector $\mathbf{A}$ , such that

$\displaystyle \mathbf{B}= \nabla \times\mathbf{A}.$

$\displaystyle \nabla ^2f = 0,$

it follows that $\nabla f$ is solenoidal.

"solenoidal field" is owned by giri.

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Other names:

solenoidal

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Cross-references: Laplace's equation, function, vector, implies, divergence, point, vector field
There are 6 references to this entry.

This is version 6 of solenoidal field, born on 2002-11-13, modified 2004-10-18.
Object id is 3590, canonical name is SolenoidalField.
Accessed 4767 times total.

Classification:

26B12 (Real functions :: Functions of several variables :: Calculus of vector functions)

Pending Errata and Addenda

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