Question

Determine whether the statement is true or false. If it is true, explainWhy. If it is false, explain why or give an example that disproves theStatement.If \({\rm{S}}\) is a sphere and \({\rm{F}}\) is a constant vector field, then \(\iint_{\text{S}} {\text{F}} \times {\text{dS = 0}}\)

Short answer

Its divergence is zero because it is a constant vector field. Hence the given statement is true.

Step-by-step solution

The divergence theorem states that.

Given that is a constant vector field, its divergence is equal to zero.

\(\begin{aligned}{}{\rm{S \bullet dS}}{{\rm{ = }}_{\rm{E}}}{\rm{divFdV}}\\_{\rm{S}}{\rm{F \bullet dS = }}\;\;\;{\rm{0dV = 0}}\end{aligned}\)

The claim true or false?

Because it is a constant vector field, the divergence is zero.

Hence, the given statement is true.