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Mathematics Question on Divergence theorem

The mathematical statement regarding Divergence theorem which is true:

A

∮SA⃗.ds=∫V⟮∇⃗×A⃗⟯dv\oint_S \vec A.ds= \int_V \lgroup \vec\nabla \times \vec A\rgroup dv

B

∮SA⃗.ds=∫V⟮∇⃗.A⃗⟯dv\oint_S \vec A.ds= \int_V \lgroup \vec\nabla . \vec A\rgroup dv

C

∫lA⃗.ds=∮V⟮∇⃗×A⃗⟯.ds\int_l \vec A.ds= \oint_V \lgroup \vec\nabla \times \vec A\rgroup .ds

D

∮VA.ds=∫V⟮∇⃗.A⃗⟯ds\oint_V A.ds= \int_V \lgroup \vec\nabla . \vec A\rgroup ds

Answer

∮SA⃗.ds=∫V⟮∇⃗.A⃗⟯dv\oint_S \vec A.ds= \int_V \lgroup \vec\nabla . \vec A\rgroup dv

Explanation

Solution

The correct option is (B): ∮SA⃗.ds=∫V⟮∇⃗.A⃗⟯dv\oint_S \vec A.ds= \int_V \lgroup \vec\nabla . \vec A\rgroup dv