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

True/False

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

Solutions

Expert Solution

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.

If you face any difficulty to understand my solution then tell me in comment otherwise like my solution. It is very good question to understand new concepts. I hope you understand my solution very easily.

milcah answered 1 year ago

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