Chapter 16.5, Problem 10E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

The vector field **F** is shown in the *xy*-plane and looks the same in all other horizontal planes. (In other words, **F** is independent of *z* and its *z*-component is 0.)

(a) Is div **F** positive, negative, or zero? Explain.

(b) Determine whether curl **F** = **0**. If not, in which direction does curl **F** point?

**10.**

(a)

To determine

**To find and explain**: The div **F**.

Explanation

**Formula used:**

Consider the standard equation of a divergence of vector field for

As **F** is independent of *z*-component

From Figure,
*z*-direction, so
*x* increases, the each vector of **F** in *x*-component increases while the *y*-component remains constant, so

Similarly, as the *y* increases, the each vector of **F** in *y*-component increases while the *x*-component remains constant, so

**(b)**

To determine

Whether

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