Question

True/False

If SS is a sphere and FF is a constant vector field, then ∬SF⋅dS=0.

Answer 1

Yes statement is true because here we use divergence theorem.

Statement of divergence theorem= E is closed region in three dimension and S is surface of Boundary of E which orientation upward then surface integral of vector field F is equal to volume of divergence (F) under E.

So here given that F is constant vector field and we know that divergence (F) =0 when F is constant vector field.

So triple integral of divergence (F) under E is equal to zero because divergence (F) is zero.

So by divergence theorem surface integral of F under S is zero always. So statement is true.

Note here we apply divergence theorem because given SS is sphere which is closed curve so divergence theorem is applicable here.

So final answer is the given statement is True.

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