Definition:Solenoidal Vector Field
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Definition
Let $\mathbf V$ be a vector field acting over a region of space $R$.
Definition 1
$\mathbf V$ is defined as being solenoidal if and only if its divergence is everywhere zero:
- $\operatorname {div} \mathbf V = 0$
Definition 2
$\mathbf V$ is defined as being solenoidal if and only if lines of flux form closed curves.
Also see
- Results about solenoidal vector fields can be found here.
Linguistic Note
The word solenoidal derives from a Greek word meaning tube.
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {V}$: Further Applications of the Operator $\nabla$: $7$. The Classification of Vector Fields