Let $\mathbf { F } ( x , y , z ) = \frac { z \mathbf { i } + x \mathbf { j } + y \mathbf { k } } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } }$ and let S be the boundary surface of the solid $E = \left\{ ( x , y , z ) \mid 1 \leq x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 4 \right\}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

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The Answer of Let $\mathbf { F } ( x , y , z ) = \frac { z \mathbf { i } + x \mathbf { j } + y \mathbf { k } } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } }$ and let S be the boundary surface of the solid $E = \left\{ ( x , y , z ) \mid 1 \leq x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 4 \right\}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

Let And Let S Be the Boundary Surface of the Solid