   Chapter 16.9, Problem 19E

Chapter
Section
Textbook Problem

A vector field F is shown. Use the interpretation of divergence derived in this section to determine whether div F is positive or negative at P1 and at P2. To determine

Whether the divergence of vector field (divF) is positive or negative at P1 and at P2 .

Explanation

If the net flow of the vectors is inward at a point P in the vector field, then the divergence of the vector field at the point P is negative and the point is called sink.

Refer to Figure in the textbook (i.e., bottom of the question 16.9-19E).

From the Figure in the textbook, the vectors enter towards the point P1 are longer than the vectors leaving from the point P1 .

As the vectors that end near the point P1 are longer than the vectors that start near the point P1 , the net flow of the vectors is inward.

Therefore, the divergence of the vector field is negative at the point P1 .

If the net flow of the vectors is outward at a point P in the vector field, then the divergence of the vector field at the point P is positive and the point is called source

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