# Volume charge density of a single point

The original problem:

I read this one, but there's something that is still unclear, even after going through all their answers and comments.

Why doesn't the expression use the 3-dimensional Dirac Delta function? That is, shouldn't the expression be: $$\rho (\overrightarrow r ) = q \delta^3 (\overrightarrow r - \overrightarrow r')$$

That's just a notational issue. $\delta(\vec{r} - \vec{r}')$ does refer to the 3D delta function, as you can tell because it has vectors inside of it. It's probably more clear to write it as $\delta^3(\vec{r} - \vec{r}')$ but it means the same thing.