If a vector field $\to A$ is said to be solenoidal, then which one of the following relation is true ?

\oint_{L} \to A . - \to d L = 0

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▽ \times \to A \neq 0

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\oint_{s} \to A . \to d s = 0

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▽ \times \to A = 0

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Solution

The correct option is C $\oint_{s} \to A . \to d s = 0$
(c)
If the divergence of a given vector is zero, then it is said to be solenoidal
$▽ . \to A = 0$
By Divergence theorem,
$\int_{v} (▽ . \to A) d v = \oint_{s} \to A . \to d s$

So, for a solenoidal field,
$▽ . \to A = 0$ and $\oint_{s} \to A . \to d s = 0$

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