- #1

PhysicsRock

- 117

- 18

- Homework Statement
- Calculate ##\displaystyle \frac{\partial}{\partial x_i} \frac{x_i}{\vert\vec{x}\vert^3}##

- Relevant Equations
- ##\nabla \cdot \vec{F} = \sum_i \frac{\partial f_i}{\partial x_i}##

As you can see in the homework statement, I am asked to calculate what's effectively the divergence of the vector field ##\vec{F} = \vec{x}/\vert\vec{x}\vert^3## over ##\mathbb{R}^3##. I have done that, the calculation itself isn't that difficult after all. However, I can't make sense of the result, which makes me wonder whether I've made a mistake. What I find is that ##\nabla \cdot \vec{F} = 0##. I used GeoGebra to plot the field, and what I see is vectors "coming out" of the origin. Is it as simple as to say that, since you can't divide by 0, the origin isn't part of the field, and thus, there is no particular source? Or have I made a mistake in my calculations and the result isn't 0?