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Chapter 14: Q. 10 (page 1150)

Give an example of a conservative vector field whose divergence is not uniformly equal to zero in $$R^{3}$$.

Short Answer

Expert verified

$$F(x, y, z)= \langle x^{2}, y^{2}, z^{2} \rangle$$ is an example of a conservative vector field whose divergence is not uniformly equal to zero in $$R^{3}$$

Step by step solution

01

Step 1. Given Information

A conservative vector field whose divergence is not uniformly equal to zero in $$R^{3}$$

02

Step 2. Explanation

Let us take an example, $$x^{2}+y^{2}+z^{2}=16$$

Here, $$F(x, y, z)= \langle x^{2}, y^{2}, z^{2} \rangle$$

Thus, $$F(x, y, z)= \langle x^{2}, y^{2}, z^{2} \rangle$$ is an example of a conservative vector field whose divergence is not uniformly equal to zero in $$R^{3}$$

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