plot a vector function

Question

Sketch the $ v = \frac {r} {r ^ 2}$ vector function and calculate its divergent. How do you plot a vector function?

Answer 1

The divergence of $\vec{v} = \frac{\hat{r}}{r^{2}}$ is easier to compute using spherical coordinates. Because $\vec{v}$ does not depend on $\theta, \phi$, its divergent is simply $$\nabla \cdot \vec{v} = \frac{1}{r^{2}}\frac{\partial}{\partial r}\bigg{(}r^{2}\frac{1}{r^{2}}\bigg{)} = 0$$