Question

For a given vector \(\vec{F}=-y\hat{i}+z\hat{j}+x^2\hat{k}\) , the surface integral \(\int_S(\vec{▽}\times \vec{F}).\hat{r}dS\) over the surface S of a hemisphere of radius R with the centre of the base at the origin is

• A. πR²
• B. \(\frac{2\pi R^2}{3}\)
• C. -πR²
• D. \(-\frac{2\pi R^2}{3}\)

Answer 1

The Correct Option is A

The correct option is (A) : πR².