Question

Given a vector field $\overrightarrow{F}$, the divergence theorem states that

• A. ${\oint }_s\overrightarrow{F}.d\overrightarrow{S}={\int }_v▽.\overrightarrow{F}dV$
• B. ${\int }_s\overrightarrow{F}.d\overrightarrow{S}={\int }_v▽\times \overrightarrow{F}dV$
• C. ${\int }_s\overrightarrow{F}\times d\overrightarrow{S}={\int }_v▽.\overrightarrow{F}dV$
• D. ${\int }_s\overrightarrow{F}\times d\overrightarrow{S}={\int }_v▽\times \overrightarrow{F}dV$

Answer 1

The correct option is A ${\oint }_s\overrightarrow{F}.d\overrightarrow{S}={\int }_v▽.\overrightarrow{F}dV$

Ans : (a)

Divergence theorem states that the volume integral of the divergence of vector field is equal to the net outward flux of the vector through the closed surface that bounds the volume. Mathematically

${\oint }_s\overrightarrow{F}.d\overrightarrow{S}={\int }_v▽.\overrightarrow{F}dV$