Chapter 16.9, Problem 20E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Are the points *P*_{1} and *P*_{2} sources or sinks for the vector field **F** shown in the figure? Give an explanation based solely on the picture.

(b) Given that **F**(*x*, *y*)* =* ⟨*x*_{,} *y*^{2}⟩, use the definition of divergence to verify your answer to part (a).

**(a)**

To determine

Whether the points

Explanation

If the net flow of the vectors is outward at a point

If the net flow of the vectors is inward at a point

Refer to Figure in the textbook (i.e., bottom of the question 16.9-20E).

From the Figure in the textbook, the vectors enter towards the point

As the vectors that end near the point

Therefore, the divergence of the vector field is positive and the point

**(b)**

To determine

**To verify:** The answers in Part (a) with the use of definition of divergence.

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P-6RECh-16 P-7RECh-16 P-8RECh-16 P-9RECh-16 P-10RECh-16 P-11RECh-16 P-12RECh-16 P-13RECh-16 P-14RECh-16 P-15RECh-16 P-16RECh-16 P-17RECh-16 P-18RECh-16 P-19RECh-16 P-20RECh-16 P-21RECh-16 P-22RECh-16 P-23RECh-16 P-24RECh-16 P-25RECh-16 P-27RECh-16 P-28RECh-16 P-29RECh-16 P-30RECh-16 P-31RECh-16 P-32RECh-16 P-33RECh-16 P-34RECh-16 P-35RECh-16 P-36RECh-16 P-37RECh-16 P-38RECh-16 P-39RECh-16 P-40RECh-16 P-41RECh-16 P-1PCh-16 P-2PCh-16 P-3PCh-16 P-5PCh-16 P-6P

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