A vector field is defined as $$\overrightarrow{f}\left ( x,y,z \right )=\dfrac{x}{\left [ x^{2}+y^{2}+z^{2} \right ]^{\frac{3}{2}}}\widehat{i}\:+\:\dfrac{y}{\left [ x^{2} + y^{2}+z ^{2}\right ]^{\frac{3}{2}}}\widehat{j}+\dfrac{z}{\left [ x^{2}+y^{2}+z^{2} \right ]^{\frac{3}{2}}}\widehat{k}$$
where $\widehat{i}, \widehat{j}, \widehat{k}$ are unit vectors along the axes of a right-handed rectangular /Cartesian coordinate system. The surface integral $\int \int \overrightarrow{f}.d\overrightarrow{S}$ (where $d\overrightarrow{S}$ is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the center, and internal and external radii of $1$ and $2$, respectively, is
- $0$
- $2\pi$
- $4\pi$
- $8\pi$