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Let G\vec { G } Be a Smooth Vector Field With divG=3\operatorname { div } \vec { G } = 3

Question 67

Essay

Let G\vec { G } be a smooth vector field with divG=3\operatorname { div } \vec { G } = 3 at every point in space.Find the exponent p in the following:  The flux of G out of any sphere of radius r1 The flux of G out of any sphere of radius r2=(r1r2)p\frac { \text { The flux of } \vec { G } \text { out of any sphere of radius } r _ { 1 } } { \text { The flux of } \vec { G } \text { out of any sphere of radius } r _ { 2 } } = \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { p }

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