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

question 14

Essay

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

---

Definitions:

Salvage Received

Salvage received refers to the amount gained or recovered from the sale or disposal of an asset after it is no longer useful or at the end of its useful life.

Simple Rate

A basic or straightforward interest rate that is applied to an amount without compounding over a time period.

Investment

The allocation of resources, such as capital or time, with the expectation of generating a future return.

Present Value

The current value of a future amount of money, calculated using a specific interest rate to account for the time value of money.