engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Calculus Multiple Integrals
The following surface integral is to be evaluated over a sphere for the given steady vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.
\(\smallint \mathop \smallint \limits_s^\; \frac{1}{4}\left( {F.n} \right)dA\) , Where S is the sphere, x2 + y2 + z2 = 1 and n is the outward unit normal vector to the sphere. The value of the surface integral is
1
π
2
2π
3
\(3\frac{\pi }{4}\)
4
4π