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solenoidal field
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(Definition)
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A solenoidal vector field is one that satisfies $$\vnabla\cdot\vB = 0$$ at every point where the vector field $\vB$ is defined. Here $\vnabla\cdot\vB$ is the divergence.
This condition actually implies that there exists a vector $\vA$ such that $$\vB = \vnabla\times\vA.$$
For a function $f$ satisfying Laplace's equation $$\vnabla^2f = 0,$$ it follows that $\vnabla f$ is solenoidal.
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"solenoidal field" is owned by giri.
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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 5762 times total.
Classification:
| AMS MSC: | 26B12 (Real functions :: Functions of several variables :: Calculus of vector functions) |
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Pending Errata and Addenda
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