Let Let S₁ Be the Sphere of Radius $5$ Centered at the Origin, Oriented Outward and Let S₂ Be

question 83

Short Answer

Let $\vec { F } = \frac { x } { \left( x ^ { 2 } + 5 y ^ { 2 } + 2 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { i } + \frac { y } { \left( x ^ { 2 } + 5 y ^ { 2 } + 2 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { j } + \frac { z } { \left( x ^ { 2 } + 5 y ^ { 2 } + 2 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { k }$ Let S₁ be the sphere of radius $5$ centered at the origin, oriented outward and let S₂ be the sphere of radius $2$ centered at the origin, also oriented outward.
Do you expect the value of $\int _ { S _ { 2 } } \vec { F } \cdot \vec { d A }$ to be larger, smaller or the same as $\int _ { S _ { 1 } } \vec { F } \cdot \vec{ d A }$ ?

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