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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

  1. $0$
  2. $2\pi$
  3. $4\pi$
  4. $8\pi$
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