A vector field is defined as\(\vec f\left( {x,y,z} \right) = \frac{x}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat i + \frac{y}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat j + \frac{z}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat k\)where î, ĵ, k̂ are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system. The surface integral \(\smallint \smallint \vec f.d\vec S\) (Where \(d\vec S\) 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 centre, and internal and external radii of 1 and 2, respectively, is

A vector field is defined as\(\vec f\left( {x,y,z} \right) = \frac{x}{

1.	A vector field is defined as\(\vec f\left( {x,y,z} \right) = \frac{x}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat i + \frac{y}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat j + \frac{z}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat k\)where î, ĵ, k̂ are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system. The surface integral \(\smallint \smallint \vec f.d\vec S\) (Where \(d\vec S\) 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 centre, and internal and external radii of 1 and 2, respectively, is
A.	0
B.	2π
C.	4π
D.	8π
Answer» B. 2π

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